Tricks of Age Questions

 Tricks

1. If present age of the father is F times the age of his son. T years hence, the father's age become Z times the age of son then present age of his son is given by [(Z - 1)T / (F - Z)]

Q. Present age of the father is 9 times the age of his son. One year later father's age become 7 times of his son. What are the present ages of the father and his son.

                a) 27              b) 30

              c) 36              d) 43

Solution 

Son's age = [( 7- 1) ×1] / [9 - 7]

                  = 6 / 2

                  = 3

So father's age = 9 × son's age

                            = 9 × 3

                            = 27 years

2. If T years earlier the age of the father was n times the age of his son, t years hence the age of the father becomes m times the age of his son then his son's age is given by

Son's age = [T ( n - 1) + t ( m - 1)] / ( n - m)

Q. 10 years ago Ravi's mother was 4 times older than her. After 10 years the mother will be twice older than the daughter. What is the present age of Ravi?

                 a) 16              b) 20

               c) 21              d) 35

Solution 

Ravi's age = [ 10 ( 4- 1) + 10 ( 2 - 1)] / ( 4 - 2)

                   = 20

3. Present age of Father : Son = a : b

After/ before T years = m : n

Then Son's age = b × [ T (m - n) / ( an - bm)] 

and father's age = a ×[T (m - n) / (an - bm)] 

Q. The ratio of the ages of the father and the son at present is 3 : 1, four years earlier, the ratio was 4 : 1. What are the present ages of the son and the father? 

Solution

Ratio of present age of father and son = 3 : 1

4 years before = 4 : 1

Son's age = 1× [ 4 ( 4- 1) / ( 4×1 - 3×1)]

                 = 12

Father's age = 3 × [ 4 (4 - 1) / (4×1 - 3×1)]

                       = 36

Shortcut tricks of Work and Wages

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এই ফেচবুক ষ্টেটাছ তোমাৰ বাবে......

 

বিদ্যা শপত খাই কৈছো, কাকো পাহৰা নাই মই। কাৰোবাক কন্দুৱাবলৈ ইচ্ছাও নাই মোৰ। ভগৱানৰ ওচৰত বিচাৰিছোঁ - যাক মই মনত পেলাওঁ, তেওঁ যাতে এনেদৰে মোক মনত পেলায়। যদিও মই জানো, সম্পৰ্ক গঢ়াটো চক পেঞ্চিলেৰে ব্লেক ব'ৰ্ডত লিখাৰ নিচিনা অাৰু সম্পৰ্ক বজাই ৰখাটো বৈ থকা পানীত পানীৰে লিখাৰ নিচিনা। হয়, নামেই নহয়। মানুহে অবয়ৱ-চেহেৰা পাহৰি যায়। সাগৰত নহয়, বহু সময়ত মানুহে চকুৰ নদীতে ডুব যায়। বিদ্যা শপত খাই কৈছোঁ - - মোৰ চকুৰ নদীত কোনেও ডুব যোৱা নাই, সকলোৱে এই নদীত সাঁতুৰিয়ে আছে। 

শিলক এনেদৰে পূজা কৰিব নালাগে যে এই শিল দেৱতা হৈ পৰে। কাকো এনেদৰে ভাল পাব নালাগে যে প্ৰবঞ্চক হৈ পৰে। চকুৰ শব্দ অন্য। চকুপানীৰ জুই অন্য। কোনেনো বিচাৰে আপোন গৰাকীৰ পৰা বিচ্ছেদ। আচলতে ভাগ্যৰ কথাই বেলেগ এক অন্য। 

প্ৰেমে দিয়া আঘাত কাকো দেখুৱাব নালাগে, কাৰণ অইনৰ হাতৰ মুঠিত থাকে যে নিমখ। বিচ্ছেদৰ ভাষাৰে নিজক নিচুকাব নালাগে, কাৰণ তেতিয়া জীবন হৈ পৰে নিৰস। 

তোমাৰ ওচৰলৈ আহিৱ নোৱাৰিলোঁ মই - - আবেলিৰ চৰাই জাকৰ সৈতে। তোমাৰ ওচৰলৈ আহিৱ নোৱাৰিলোঁ মই শীতৰ ৰ'দজাকৰ দৰে। মই হব নোৱাৰিলোঁ তোমাৰ বসন্তৰ কুলি। কব নোৱাৰিলোঁ বহু কথা খুলি। হয়, দিন গল গলি গলি। সেয়ে অৱশ্যে চিয়াঁহিৰে মই লিখোঁ জীবন যৌৱনৰ চকুলো। 

বিদ্যা শপত খাই কৈছোঁ--- সাগৰৰ পানী মিঠা নোহোৱালৈকে কাকো নাপাহৰোঁ। নৈ হৈ বৈ থাকিম। নিৰৱধি। হয়, কাকো পাহৰা নাই মই। ভগৱানৰ ওচৰত বিচাৰিছোঁ, 'যাক মই মনত পেলাওঁ, তেওঁ যাতে মোক এনেদৰে মনত পেলায়'। 

বৰ্ষাৰণ্য আপুনি কিয় চোৱা উচিত? 

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'বৰ্ষাৰণ্য' আপুনি কিয় চোৱা উচিত ?

প্ৰকৃতিপ্ৰেমীৰ বাবে এখন অসমীয়া চলচ্চিত্ৰ 'বৰ্ষাৰণ্য'

১)বৰ্তমান সময়ত আপুনি বাতৰি কাকত অথবা টেলিভিছন চেনেলৰ দ্বাৰা বন বিভাগৰ নগ্ন স্বৰূপ সংক্ষিপ্ত বাতৰি আকাৰে পাই আহিছিল। বৰ্ষাৰণ্য'ত ইয়াক বিস্তৃত ৰূপত দেখিবলৈ পাব। 

২)কিছুমান বিলুপ্তপ্ৰায়ী প্ৰাণীয়েই হওক বা কেৱল বৰ্ষাৰণ্যত উপলব্ধ হোৱা 'জুৱেল' অৰ্কিডেই হওক, প্ৰকৃতিৰ বিষয়ে কিছুমান নজনা কথা জানিব পাৰিব। বিশেষকৈ শিক্ষাৰ্থী সকলে বৰ্ষাৰণ্যৰ সৃষ্টি, গঠন আদিৰ বিষয়ে জনাত সুবিধা হব। 

৩) ছবিখন চোৱাৰ পাছত ক্ৰমাৎ বৃদ্ধি পাবলৈ ধৰা বনধ্বংস ৰোধ কৰিবলৈ আপুনিও আগবাঢ়ি আহিবলৈ বাধ্য হব। সামগ্ৰিক ভাৱে প্ৰকৃতিপ্ৰেমীৰ বাবে বৰ্ষাৰণ্য উৎকৃষ্ট ছবি। 

Tricks of VARIATION and PARTNERSHIP 

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Tricks of VARIATION AND PARTNERSHIP

Shortcut Tricks of Partnership

1. Two numbers are in the ratio a : b. If p is added to the first number and q is added to the second number respectively, then ratio of the resulting numbers become    m : n. Then 

the original first number

                    = [ a (mq - np) ] / (an - bm) 

the original second number 

                    =[ b (mq - np)] / (an - bm) 

Q. In the class, the number of boys and girls is in the ratio of 4 : 5. If 10 more boys join the category, the ratio of numbers of boys and girls becomes 6 : 5. How many girls are there in the class? 

              a) 20               b) 30

             c) 25                d) Couldn't be determined 

Solution : c)

Number of girls = [b (mq - np)] / (an - bm) 

                              = [5 ( 6 ×0 - 5× 10)]/ ( 4×5 - 5×6) 

                              = 25

2. If on adding x to four numbers a, b, c, d; the resulting numbers become proportional then

         x = (bc - ad) / [(a + d) - (b + c)] 

Q. What must be deducted from each of the numbers 7,10,12 and 18 so that the resultant numbers are in proportion? 

               a) 1              b) 2

               c) 3              d) 4

Solution : b) 

Required number = (bc - ad) / [ (a + d) - ((b + c)] 

                     = ( 10×12 - 7 ×18) / [( 7 + 18) - ( 10 + 12)]

                     = - 6/3

                     = - 2

Thus 2 must be subtracted from each of the numbers. 

3. The ratio between two numbers is a : b, if each number is increased by x, the ratio becomes c : d. 

Then sum of two numbers 

                 = [x (a + b) (c - d)] /(ad - bc) 

Q. Two numbers are within the ratio 2 : 3. If 4 be added to both of them, then their ratio becomes 3 : 4. Find the sum of the numbers 

               a) 10             b) 15

              c) 20              d) 25

Solution : b) 

Sum of two numbers = [ 4 (a +b) (c - d)] /(ad - bc) 

                     = [ 4 (2 + 3) ( 3 - 4)] / (2×4 - 3×3)

                     = 20

COMPUTER AWARENESS

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Problems on Work and Wages

Problems on Work and Wages with explanation

Q. A can do a piece of work in 3 days while B can do the same work in 4 days. If they work together for a total wages of 2800, how much does A get? [Bank Clerks 2009]
Solution
A's 1 day's work = 1/ 3
B's 1 day's work = 1 /4
A's share : B's share
   = 1 / 3 : 1 / 4
   = 4 : 3
A's share = 4/7 × 2800
                = 1600

Q. A alone can do a piece of work in 3 days, while B alone can do the same work in 2 days. If they work together to complete the work, their total wages is fixed 225. Find the share of A. [RRB 2008]
Solution
A's 1 day's work = 1 / 3
B's 1 day's work = 1 / 2
A's share : B's share = 1 / 3 : 1 / 2
                                 = 2 : 3
Share of A = 2 / 5 × 225
                  = 90


Q. A alone can finish a work in 2 days, while B alone can finish it in 3 days. If they work together to finish it, then out of total wages of 6000, what will be the 20% of A's share? [Hotel Mgmt. 2009]
Solution
A's 1 day's work = 1/ 2
B's 1 day's work = 1 /2
A's share :B's share = 1 / 2 : 1 / 3
                       = 3 : 2
Therefore
A's share = (3 / 5) × 6000
                = 3600
Therefore 20% of A's share = 3600 × 20 / 100
                                    = 720
Q. Vandana can do a piece of work in 10 days. With the help of Ruchi, she can do the same work in 6 days. If they get 200 for that work, then what will be the share of Ruchi in the received remuneration?
Solution
Vandana's 1 day work = 1/10
( Vandana + Ruchi)'s 1 day's work = 1 / 6
Therefore Ruchi' s 1 day's work = 1/ 6 - 1/10
                                 = 4/60 = 1/15
Ratio of wages of Vandana and Ruchi
                     = 15 : 10
Ruchi's wages ={A /( A + B)} × total wages
                        = (10 / 25) × 200
                        = 80

Q. A sum of money is sufficient to pay A's wages for 21 days and B's wages for 28 days. The same money is sufficient to pay the wages of both for [SSC CCL 2013]
Solution
A's 1 day's work = 1 / 21
B's 1 day's work = 1 / 28
Therefore same money is sufficient to pay the wages of both for = 1 / { (1/21) + (1/28)}
     = (21 × 28)/ 49
     = 3× 4
     = 12 days

Shortcut tricks of Work and Wages

Shortcut tricks of Time and Work problem 

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Shortcut tricks on WORK AND WAGES

Fast Track Formulae to solve the QUESTIONS on Work and Wages

1.If A and B can do a piece of work in x and y days respectively, the ratio of their wages will be y: x. Then, the wages earned by A and B will be
    A's wages = {Total wages /(x + y)} × y
    B's wages = { Total wages / ( x + y)} × x

Q.Akansha can do a piece of work in 6 days, while Vasudha can do the same work in 5 days. If the total amount to be given for this work is 660, then what will be the share of Vasudha, if both work together.
Solution
Time taken by Akansha = 6 days
Therefore 1 days work = 1 / 6
 And
Time taken by Vasudha = 5 days
Therefore 1 days work = 1 / 5

Total amount earned = 660
Ratio of their incomes = 1 / 5 : 1 / 5 = 5 : 6
Therefore
 Vasudha's share ={660 / (5 + 6)} × 6
                            = 360

2. A can do a piece of work in x days. With the help of B, A can do the same work in y days. If they get a for that work, then
Share of A = ay / x
Share of B = a ( x - y) / x

Q. Suresh can do a work in 20 days. Suresh and Surendra together do the same work in 15 days. If they got 400 for that work, then find the share of Suresh and Surendra?
Solution
Here x = 20, y = 15, a = 400
Now, according to the formula
Share of Suresh = ay / x
                           = 400 × 15 / 20
                           = 300
Share of Surendra = a ( x - y) / x
                            = 400 ( 20 - 15) / 20
                            = 100


3. X, Y and Z undertake to do a work for R. If together they do only m/n of the work and rest is done by C alone, then the share of C is given by
                R ( 1 - m / n)

Q. A, B and C undertake to do a work for 480. A and B together do 1/4 of the work and rest is done by the C alone. How much should C get?
Solution
Here R = 480, m = 1, n = 4
Now according to the formula
Share of C = R ( 1 - m / n)
                  = 480 ( 1 - 1 / 4)
                  = 360

Q. Shantanu can do a piece of work in 12 days and Manu can do the same work in 10 days. If they work together, in what ratio Shantanu and Manu will receive their wages?
Solution
Shantanu's 1 day's work = 1 / 12
Manu's 1 day's work = 1/10
Shantanu's share : Manu's share
        = 1/12 : 1/10
        = 10 : 12
        = 5 : 6

Q. A alone can do a piece of work in 8 days while B alone can do it in 10 days. If they together complete this work and get 900 as their remuneration, then find the shares of both the persons.
Solution
Ratio of wages of A and B = 10 : 8
A's wages = { A / (A + B)} × total wages
                 = {10 / (10 + 8)} × 900
                 = 500
Similarly
B's wages = { 8 / (10 + 8)} × 900
                 = 400

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Computer Awareness

Computer Awareness

1.To perform calculation on stored data computer uses…… number of system. [SBI CLERK 2009]
      A. Decimal. 
      B. Hexadecimal.
      C. Octal.     
      D. Binary
      E. None of these
Answer D. Binary

2.A hexadecimal number is represented by
      1. Three digits.
      2. Four binary digits.
      3. Fiur digits.
      4. All of these
      5. None of these
Answer 2. Four binary digits

3.What is the value of binary number 101?
      A.  3         B. 5
      C.  6         D. 101
Answer 2. 5

4.Which of the following is an example of binary number
      A. 6AH.
      B. 10100
      C. 005.
      D. G3Do
      E. All of these
Answer B. 10100

5.Which of the following is not a binary number?
      A. 001.           B. 1010
      C. 203.           D. 10010
Answer C. 203

6.How many values can be represented by a single byte?
      A. 4             B. 16
      C. 64.          D. 256
Answer D. 256

7.The binary equivalent of decimal number 98 is [IBPS CLERK 2012]
      A. 1110001           B. 1110100
      C. 1100010           D. 1111001
Answer C. 1100010

8.MSD refers as
          A. Most significant digit
          B. Many significant digit
          C. Multiple significant digit
          D. Most Significant Decimal
          E. None of these
Answer A. Most significant digit

9.Binary system is also called
       A. Base one system
       B. Base two system
       C. Base system
       D. Binary system
       E. None of these
Answer B. Base two system

10.The most widely used code that represents each character as a unique 8 bit code is
       A. ASCII
       B. UNICODE
       C. BCD
       D. EBCDIC
       E. None of these
Answer A. ASCII

11.What type of information system would be recognised by digital circuits?
        A. Hexadecimal system
        B. Binary system
        C. Both '1' and '2'
        D. Only roman system
Answer C. Both '1' & '2'

12.The negative numbers in the binary system can be represented by
     A. Sign magnitude
     B. 1's compliment
     C. 2's compliment
     D. All of these
     E. None of these
Answer D. All of these

Practice questions on Time and Work problem

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Shortcut tricks of Time and Work problem


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Practice questions on Time and Work problem

Practice questions on Time and Work problem

1.If the work done by 8 men and 4 boys in 1 day is 7 times the work done by 1 man and 1 boy, then compare the work done by 1 man and 1 boy in 1 day? [CDS 2013]
Solution
Here a = 8, b = 1, x = 4, y = 1, n = 7
Therefore
Work done by 1 man / work done by 2 boy
      = (ny - x) / ( a - nb)
      = ( 7 × 1 - 4) / ( 8 - 7× 1)
      = 3 / 1
   

2.If 14 men and 12 boys can finish work in 4 days, while 8 men and 16 boys can finish the same work in 5 days. Compare the 1 day work of 1 man and 1 boy.
Solution
Here a = 14, b = 12, x = 4, y = 5, c = 8, d = 16
One day work of 1 man / one day work of 1 boy
     = ( yd - xb) / ( xa - yc)
     = ( 5 × 16 - 4 × 12) / ( 4 × 14 - 5 × 8)
     = 32 / 16
     = 2 / 1

3.A stock of food is enough for 240 men for 48 days. How long will the same stock last for 160 men? [CDS 2012]
Solution
Given M1 = 240, D1 = 48,
          M2 = 160, D2 =?
  Therefore M1 D1= M2 D2
           240 × 48 = 160 × D2
           D2 = 240 × 48 / 160
                = 72

4.45 people take 18 days to dig a pond. If the pond would have to be dug in 15 days, then the number of people to be employed will be [CDS 2012]
Solution
Given M1 = 45, D1 = 18
           M2 =?, D2 = 15
Therefore M1 D1= M2 D2
             45 × 18 = M2 × 15
             M2 = 54

5.A certain number of men can do a piece of work in 80 days. If there were 10 men less, It could be finished in 20 days more. How many men are there in the starting?
Solution
Here a = 10, D =80, d = 20
Therefore number of men in starting
            = a (D + d) / d
            = 10 × ( 80 + 20)/ 20
            = 50

6.20 workers working for 5 h per day complete a work in 10 days. If 25 workers are employed to work 10 h per day, what is the time required to complete the work? [CDS 2013]
Solution
Here M1 = 20, M2 = 25, T1 = 5, T2 = 10, D1 = 10, D2 =?
Therefore M1× D1 × T1= M2× D2× T2
                20 × 10 × 5 = 25 × D2 × 10
                D2 = 4
Therefore D2 = 4 days

7.A contractor undertook to do a certain piece of work in 18 days. He employed certain number of men but 12 of them being absent from the very 1st day, the rest could finish the work in 30 days. Find the number of men originally employed.
Solution
Let the number of men at the beginning = x
Given M1 = x, M2 = x - 12, D1 = 18, D2 =30
According to the formula
       M1 D1 = M2 D2
       x × 18 = (x - 12) × 30
       2x = 60
         x = 30


Shortcut tricks of Time and Work problem 

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Tricks of Time and Work problem

Tricks

1. If A can do a piece of work in x days and B can do the same work in y days then time taken by (A + B) to complete the work = xy / (x + y) days

Q. A can do a piece of work in 10 days and B can do the same work in 12 days. How long will they take to finish the work, if both work together?

Solution 

Here x = 10, y = 12

Therefore number of days taken by A and B 

             = 10 × 12 / (10 + 12)

             = 120 / 22

             = 60/11 days

2. If A can do a piece of work in x days, B can do the same work in y days and C can do the same work in z days then time taken by (A + B + C) to complete the work

                     = xyz / (xy + yz + zx) days

Q. If A can do a piece of work in 4 days, B can do the same work in 8 days and C can do the same work in 12 days, then working together, how many days will they take to complete the work?

Solution 

Here x = 4, y = 8, z = 12

Therefore number of days taken by ( A+ B+ C)

                    = 4 × 8 × 12 / (4 × 8 + 8 × 12 + 12 × 4)

                    = 32 × 12 / ( 32 + 96 + 48)

                    = 384 / 176

                    = 24 / 11

3. If A and B can complete a work in x days and A alone can finish that work in y days, then number of days required to complete the work by B = xy / (y - x) days

Q. A and B together can do a piece of work in 12 days and A alone can do it in 18 days. In how many days can B alone do it?

Solution 

Here x = 12, y = 18

Time taken by B = 12 × 18/ (18 - 12)

                           = 36 days

4. If A can do a work in x days and B can do y% fast than A, then B will be complete the work in 100x / (100 + y) days

Q.Kamal can do a work in15 days and Vimal is 50% more expert than Kamal to complete the same work, then find total time taken to complete the work by Vimal.

Solution 

Here x = 15, y = 50%

Now, time taken by Vimal = 100x / (100 + y) 

                  = 100 × 15 / (100 + 50)

                  = 1500 / 150

                  = 10 days

5. A and B do a piece of work in a and b days, respectively. Both begin together but after some days, A leaves off and the remaining work is completed by e in x days. Then, the time after which A left, is given by T = (b - x) a / (a + b) 

Q. A and B can do a piece of work in 40 days and 50 days, respectively. Both begin together but after a certain time, A leaves off. In this case B finishes the remaining work in 20 days. After how many days did A leave?

Solution 

Here a = 40, b = 50, x = 20, T =?

     T = ( 50 - 20) × 40 / ( 40 + 50)

        = 30 × 40 / 90

        = 40 / 3 days

Q. A and B together can do a piece of work in 12 days, while B alone can finish it in 30 days. A alone can finish the work in [SSC (10+2) 2012]

Solution 

Here x = 12, y = 30

Required number of days

          = 12 × 30/(30 - 12) 

          = 360 / 18

          = 20 days

Practice questions on Partnership 

Practice questions on Ages

Shortcut Tricks of Problem on Ages

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practice questions on Partnership

1.Srikant and Vividh started a business investing amounts of 185000 and 225000, respectively. If Vividh's share in the profit earned by them is 9000, what is the total profit earned by them together? [Bank Clerks 2009]

Solution
Ratio of profit = Ratio of investment
Therefore Srikant's share : Vividh's share
              185000 : 225000 = 37 : 45
Let Srikant's share = 37x
        Vividh's share = 45x
According to the question
          45x = 9000
              x = 200
Therefore total profit
            = 37x + 45x
            = 37 × 200 + 45 × 200
            = 7400 + 9000
            = 16400

2. Rajan and Sajan started a business initially with 14200 and 15600, respectively. If total profits at the end of year is  74500, what is the Rajan's share in the profit? [Bank Clerks 2009]

Solution
Ratio of profit of Rajan abd Sajan = Ratio of their                                                                                     investment
                             = 14200 : 15600
                             = 71 : 78
Therefore Rajan's share = [ 71 / (71 + 78)] × 74500
                                            = 35500

3. A starts a business with  4000 and B joins him after 3 months with  16000. Find the ratio of their profits at the end of year.

Solution
A's share : B's share
= Ratio of product of investment and tine period of investment
= 4000 × 12 : 16000 × ( 12 - 3)
= 4 × 12 : 16 × 9
= 1 : 3

4.A starts a business with 9000 and B joins him after 6 months with an investment of 45000. What will be the ratio of the profits of A and B at the end of year? [Hotel Mgmt. 2008]

Solution
      A's share : B's share
   = 9000 × 12 : 45000 × ( 12 - 6)
   = 12 : 5 × 6
   = 2 : 5

5. X starts a business with 300000 and Y joins him after 3 months with 1200000. Find the ratio of their profits at the end of the year. [Bank Clerks 2011 ]

Solution
      X's share : Y's share
    = (300000 × 12) : ( 1200000 × 9)
    = 36 : 108
    = 1 : 3

6. Ram, Shyam and Kamal together start a business in partnership. The ratio of their capitals is 3 : 4 : 7. If their annual profit be 21000, what will be Kamal's share in this profit? [RRB 2007]

Solution
Given ratio of profits of Ram, Shyam and Kamal
                     = ratio of their capitals
                     = 3 : 4 : 7
Kamal's share =[ 7 / ( 3 + 4 + 7)] × 21000
                          =  ( 7 / 14) × 21000
                          = 10500
7. Rakesh, Dinesh and Mahesh start a business by investing 5000, 8000 and 12000, respectively. At the end of year, they got the profit of 12500. What is the share of Dinesh in profit? [RRB CCL 2012]

Solution
Share of Rakesh :Share of Dinesh : Share of Mahesh
   = 5000 : 8000 : 12000
   = 5 : 8 : 12
Total earned profit = 12500
Therefore
Share of Dinesh in profit
       = [ 8 / ( 5 + 8 + 12)] × 12500
       = ( 8 / 25) × 12500
       = 8 × 500
       = 4000

8. A and B invest in the ratio of 3:5, respectively. After 6 months, C enters the business with the investment of the capital equal to that of B. What will be the ratio of the profits of A, B and C at the end of year? [SSC LDC 2008]

Solution
Let investment of A = 3x
       investment of B = 5x
       Investment of C = 5x
As we know
   Ratio of profit = Ratio of investment
 A's share : B's share : C's share
 3x × 12 : 5x × 12 : 5x × (12 - 6)
= 3x × 12 : 5x × 12 : 5x × 6
= 6 : 10 : 5

Practice questions on ages

Tricks of problems on Ages

Questions on Unitary Method

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Practice questions on Ages

1.The average age of 8 children of a family is 12 yr. If the age of 7 children are 12, 8, 14, 11, 9, 13 and 15 yr, then the age of 8th child will be [RRB 2008]

Solution

Since total age of 8 children =  8 × 12

                                                    = 96 yr

and total age of 7 children 

 = 12 + 8 + 14 + 11 + 9 + 13 + 15

 = 82 yr

Therefore the age of 8th children

              = 96 - 82

              = 14 yr

2. The ratio between the present ages of A and B is 4: 5. If the ratio between their ages 4 yr hence becomes 14:17, then what is B's age at present? [RRB 2009]

Solution 

Let the ages of A and B are 4x and 5x respectively 

A/Q, (4x + 4) / ( 5x + 4) = 14 / 17

         68x + 68 = 70x + 56

         2x = 12

           x = 6

Therefore present age of B =5 × 6 = 30 yr

3. In a family, the average age of father and mother is 35 yr. The average age of the father, mother and their only son is 27 yr. What is the age of the son? [SSC CGL 2010]

Solution 

Since total age of father and mother = 35 × 2

                                                                   =70 yr

and total age of father, mother and son

                               = 27 × 3

                               = 81 yr

Therefore age of son = 81 - 70

                                       = 11 yr

4.The average age of 9 students and their teacher is 16 yr. The average age of the first four students is 19 yr and that of the last five is 10 yr. The teacher's age is [SSC (10+2) 2010]

Solution 

Since total age of 9 students and a teacher 

                   = 10  × 16

                   = 160 yr

Total age of first 4 students = 4 × 19

                                  = 76 yr

and total age of last 5 students = 5 × 10

                                                         = 50 yr

Therefore age teacher = 160 - 76 - 50

                                         = 34 yr

5.At present, Anil is 1.5 times of Purvi's age. 8 yr hence, the respective ratio between Anil and Purvi's ages will be 25: 18 What is Purvi's present age? [IBPS Clerk 2011]

Solution 

Let age of Purvi = x yr

Then age of Sunil = 1.5 x yr

According to the question 

        (1.5x + 8) / (x + 8) = 25 / 18

         27x + 144 = 25x + 200

            2x = 56

              x = 28

Hence present age of Purvi = 28 yr

6.The average of the present ages of Sachin and Saurabh is 36 yr. If Sachin is 8 yr older than Saurabh, what is the Saurabh's present age? [Allahabad Bank Clerk 2010]

Solution 

Since total age of Sachin and Saurabh 

                 = 36 × 2

                 = 72

Let age of Saurabh = x yr

Then age of Sachin = x + 8 

According to the question 

              x + x + 8 = 72

                       2x = 64

                         x = 32

Hence Saurabh's present age = 32 yr

7. At present Meena is eight times her daughter's age. 8 yr from now, the ratio of the ages of Meena and her daughter will be 10:3, respectively. What is Meena's present age? [IDBI PO 2009]

Solution 

Let age of daughter = x yr

Age of Meena = 8x yr

According to the question 

       (8x + 8) / ( x + 8) = 10 / 3

        24x + 24 = 10x + 80

        14x = 56

            x = 4

Hence Meena's present age = 4 × 8

                                                  = 32 yr

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Shortcut tricks of Problem on ages

Tricks

1.If ratio of present ages of A and B is x: y and n yr ago, the ratio of their ages was p : q then (x - n) /( y - n) = p/q
Q. A father is twice as old as his son. 20 yr back, he was twelve times as old as his son. What is the present age of father?
Solution
Let the present age of father be 2k yr and that of son is k yr
Then x = 2k and y = k
Also, 20 year before the ratio of their ages was 12 : 1
So p / q = 12 / 1
Then (x - n) /(y - n) = p / q
           (2k - 20) / (k - 20) = 12 / 1
             2k - 20 = 12k - 240
             10k = 220
                 k = 22
Therefore present age of father = 2 × 22 = 44 yr

2. If ratio of present ages of A and B is x: y and after n yr, the ratio of their ages will be p : q then
               ( x + n) / (y + n) = p / q

Q. I am three times as old as my son. 15 yr hence, I will be twice as old as my son. What is the sum of our present ages.
Solution
Let the present ages of man and his son be 3k and k yr respectively
So x = 3k and y = k
Also p / q = 2 / 1
Then (x + n) / (y + n) = p / q
          (3k + 15)/ ( k + 15) = 2 / 1
          3k + 15 = 2k + 30
          k = 15
Therefore sum of their ages = 3k + k = 4k = 4 × 15 = 60

3.If M is as elder to N as he is younger to P and sum of ages of N and P is t yr, then N<M<P
M's age = sum of ages of N and P / 2 = S / 2
                 where S = sum

Q. If Akshay is as much elder than Vinay as he is younger to Kartik and sum of ages of Vinay and Kartik is 48 yr, then find the age of Akshay.
Solution
Present age of Akshay = sum of ages / 2
                                         = 48 / 2 = 24 yr

4. The present ages of Reena and Usha are 24 and 36 yr, respectively. What was the ratio between the ages of Usha and Reena respectively 8 yr ago?
Solution
Required ratio = ( 36 - 8) / ( 24 - 8)
                            = 28 / 16
                            = 7 : 4

5.Raju decided to marry 3 yr after he gets a job. He was 17 yr old when he passed class 12th. After passing class 12th, he had completed his graduation course in 3 yr and PG course in 2 yr. He got the job exactly 1 yr after completing his PG course. At what age will he get married?
Solution
Since age of Raju when he got the job
                   = 17 + 3 + 2 + 1
                   = 23
Therefore age of Raju at the time of marriage
                   = 23 + 3 = 26 yr

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Practice questions on Unitary method

1. If cost of 24 oranges is  72, then find out the cost of 120 oranges. [Bank Clerks 2009]

Solution
Given cost of 24 oranges = 72
            Cost of 1  orange   = 72/24
                                             = 3
Therefore
       Cost of 120 oranges = 3 × 120
                                           = 360

2. If cost of 15 eggs is 75, then find out the cost of 4 dozens eggs. [Bank Clerks 2010]

Solution
Given cost of 15 eggs = 75
            Cost of 1 egg    = 75/15
                                       = 5
Therefore
     Cost of 4 dozens ( 4× 12 = 48) eggs
                                        = 5 × 48
                                        = 240

3. A worker makes a toy in every 2 h. If he works for 80 h, then how many toys will he make? [Hotel Mgmt. 2008]

Solution
Let number of toys be x
More hours, more toys (Direct proportion)
                  2 : 80 :: 1 : x
                 x = 80/2
                    = 40 toys

4. 12 men can do a piece of work in 24 days. How many days are needed to complete the work, if 8 men are engaged in the same work? [IDBI Officers 2010]

Solution
Since 12 men can do the work in 24 days
Therefore 1 man will do it in 12  × 24 days
   8 men will do it in (12 × 24) / 8 days
                                     = 36 days
 Hence required number of days  = 36 days

5. If 45 m of a uniform rod weights 171 kg, then what will be the weight of 12 m of the same rod? [MBA 2008]

Solution
Since weight of 45 m rod = 171 kg
Therefore weight of 1 m rod = 171/45 kg
Weight of 12 m rod =( 171 /45) × 12
                                    = 45.6 kg
6.  22 men can complete a job in 16 days. In how many days, will 32 men complete that job? [Bank Clerks 2009]

Solution
Since  22 men do the work in 16 days
Therefore 1 man will do the work in 16 × 22 days.
   32 men will do the job in (16 × 22)/32 days
                                                   = 11 days
Therefore required number of days = 11 days

7.If in a hostel, food is available for 45 days for 50 students. For how many days will this food be sufficient for 75 students? [CGPSC2013]

Solution
Since for 50 students, food is sufficient for 45 days
For 1 student, food is sufficient for 45 × 50 days
Therefore for 75 students, food is sufficient for (45 × 50)/75
                             = 30 days

8.In a garrison, there was food for 1000 soldiers for one month. After 10 days, 1000 more soldiers joined the garrison. How long would the soldiers be able to carry on with the remaining food? [CSAT2013]

Solution
Since for 1000 soldiers, remaining food is sufficient for
                               30 - 10 = 20 days
Therefore for 1000 + 1000 = 2000 soldiers, food will be sufficient for  (1000 / 2000) ×20 = 10 days

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Shortcut tricks of Compound Interest

Tricks

Let principal =P
Rate =R%
Time=n years

1.If interest is compounded annually, then
               Amount=P(1+R/100)^n

Compound Interest= Amount –Principal

Compound Interest= P[(1+R/100)^n - 1]

2.If the interest is compounded half-yearly ,then R=R/2       & n=2n then
                  Amount=P(1+R/2 × 100)^2n

3.If the interest is compounded quaterly, then R=R/4 & n=4n
    then Amount=P(1+R/4  × 100)^4n

4. If interest is compounded (1+{(a/b)R }/ 100)

5.If rates of interest are R1%, R2% and R3% for 1st,2nd and 3rd year respectively,then

Amount=P(1+R1/100) (1+R2/100)( 1+R3/100)

Q. Find the compound interest on Rs 8000 at 4% p.a for 2yrs compounded annually.

Solution: Given that P=Rs 8000

R=4%

Time= 2year

Now according to the formula,

Amount= P(1+R/100)^n

= 8000(1+4/100)^2

=8000 x 26/25 x 26/25

=Rs. 8652.80

Therefore, CI=Amount – principal

=Rs.8652.80 – Rs. 8000

=Rs.652.80

Q. Ruchi invested Rs. 1600 at the rate of compound interest for 2 years. She got Rs. 1764 after the specific period. Find the rate of interest

Solution : Given that P=Rs 1600

Time= 2year

Amount= Rs 1764

Now according to the formula,

Amount= P(1+R/100)^n

1764=1600(1+R/100)^2

1760/1600 = (100+R/100)^2

441/400 = (100+R/100)^2

(21/20)^2=(100+R/100)^2

100+R/100 = 21/20

100 + R=21/20 X 100

100 + R= 105

R= 105 – 100=5%

Q. Find the compound interest on Rs5000 in 2years at 4%, if the interest being compounded half-yearly.

Solution: Given that P = Rs 5000

R=4%

Time= 2year

Now according to the formula,

Amount= P(1+R/2 x 100)^2n

= 5000(1+4/100)^4

=5000 x 51/50 x 51/50 x 51/50 x 51/50

=51 x 51 x 51 x 51 / 1250

=Rs. 5412.16

Therefore, CI=Amount – principal

=Rs.5412.16 – Rs. 5000

=Rs.412.16

Q. Find the compound interest on Rs8000 in 9months at 20%, if the interest being compounded quarterly.

Solution: Given that P = Rs 8000

R=20%

Time= 9 months = ¾ year

Now according to the formula,

Amount= P(1+R/4 x 100)^4n

= 8000(1+20/400)^(3/4 x4)

= 8000(1+5/100)^3

=8000 x 21/20 x 21/20 x 21/20

=Rs. 9261

Therefore, CI=Amount – principal

=Rs.9261 – Rs. 8000

=Rs.1261

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