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

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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

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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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Shortcut tricks of True discount and Banker's Discount

Tricks

1. If rate of interest is R% per annum, time is T yr and present worth is PW, then true discount (TD)
                            = PW × R × T / 100

2. If rate of interest is R% and money due (for amount) is A after T yr. then
           Present Worth (PW) =  100 × A / ( 100 + R × T)

3. If money due A, rate of interest R% and time T are given, then true discount (TD) = A × T × R / ( 100 + R × T)

4.If the face value A, remaining time T and rate R% are given, then Banker's Discount (BD) = A × R × T / 100

5. If the face value of a bill due T yr hence is A and rate is R%, then Banker's Gain (BG) = TD × TD /PW

6. If the true discount at a bill due T yr hence is TD and annual rate of interest is R%, then Banker's Gain (BG)
                     = TD × R × T / 100

7. If the face value on a bill is A and true discount is TD
       then BD = A × TD / (A - TD)
Q. What will be the true discount for the present worth of  6000 for a period of 9 months at 12% per annum?

Solution Given that T = 9 month = 9 / 12 yr
                                    R = 12%, PW = 6000
Therefore TD = PW × R × T / 100
                         = 6000 × 12 × (9/12) / 100
                         = 60 × 9 = 540

Q. Find the present worth of  1860 due 3 yr hence at 8% per annum. Also, find the true discount.

Solution Given that A = 1860, R = 8%, T =3 yr
According to the formula,
           PW =    100 × A / ( 100 + R × T)
                   = 100 × 1860 / ( 100 + 8 × 3)
                   = 100 × 1860 / 124
                   = 1500
           TD = A - PW
                 = 1860 - 1500
                 = 360

Q. Find the sum due, if the true discount on a sum due 2 yr hence at 14% rate of interest be  336.

Solution Given that T = 2 yr, R = 14%, TD = 336
        Sum due(A) =?
According to the formula,
   true discount (TD) = A × T × R / ( 100 + R × T)
                              336 = A × 2 × 14 /( 100 + 14 × 2) = 28A / 12      Therefore               A = 1536

Q. Find the banker's discount at a bill of  25500 due 2 months hence, when rate of interest is 3% per annum.

Solution Given that A = 25500, R = 3%,
    T = 2 months = 2/12 = 1/6 yr, BD =?
According to the formula,
                   (BD) = A × R × T / 100
                            = 25500 × 3 × (1/6)/100
                            = 127.5

Q.The true discount at a bill of  3720 due 8 months hence is 120. Find the banker's gain.

Solution
Present Worth of bill = 3720 - 120 = 3600
  Therefore Banker's Gain (BG) = TD × TD /PW
                                         = 120 × 120 / 3600
                                         = 144 / 36 = 4

Q. If the banker's gain is 180 at a bill due 6 yr hence at 10% per annum, find the banker's discount.

Solution Given that BG = 180, R = 10%, T = 6yr
According to the formula,
                 BG = TD × R × T / 100
                180 = TD × 10 × 6 / 100
                 TD = 300
As we know that BG = BD - TD
                                BD = BG + TD = 180 + 300 = 480

Q.The true discount on a bill of 900 is 100. Find the banker's discount.

Solution Given
                A = 900,  TD = 100
According to the formula
               BD = A × TD / (A - TD)
                     = 900 × 100 / (900 - 100)
                     = 112.5

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Computer awareness set - 4

1. Which is not an integral part of computer? [ SBI CLERK 2012]
                       a. CPU.            b. Mouse
                       c. Monitor.     d. UPS
                       d. None of these
Answer : d. UPS

2. Microprocessors can be used to make [SBI CLERK 2009]
                       a. Computer.            b. Digital system
                       c. Calculators.          d. All of these
                       e. None of these
Answer : d. All of these

3. 'C' in CPU denotes.  [SBI PO 2011]
                   a. Common.          b. Central
                   c. Convenient.      d. Computer
                   e. Circuitry
Answer : b. Central

4. The communication line between CPU memory and peripherals is called a [UBI Clerk 2011]
                    a. Bus.            b. Line
                    c. Media.       d. All of these
                    e. None of these
Answer : a. Bus

5. The first microprocessor was
                    a. Intel 4004.            b. 8080
                    c. 8085.                      d. 4008
                    d. 8081
Answer :  a. Intel 4004

6. Where does computer add and compare data?
                    a. Hard disk.             b. Floppy disk
                    c. CPU chip.               d. Memory chip
                    e. None of these
Answer : c. CPU chip

7. The control unit controls other units by generating [IBPS Clerk 2011]
                    a. Control signals.              b. Timing signal
                    c. Transfer signal.              d. Command signal
                    e. None of these
Answer : a. Control signal

8. CPU can directly understand this language [PNB clerk 2010]
                 a. C.                                      b. Assembly
                 c. Machine language.       d. Java
                 e. None of these
Answer : c. Machine language

9. The main circuit-board of the system unit is [IBPS CLERK 2011]
                 a. Computer program.                b. Control unit
                 c. Motherboard.                           d. RAM
                 e. None of these
Answer : c. Motherboard

10.  The types of input include
                   a. Data.                b. Programs
                   c. Commands.    d. User response
                   e. All of these
Answer : e. All of these

11. The basic goal of computer process is to convert the data into [SBI PO 2012]
                    a. Files.                    b. Tables
                    c. Information.      d. Graphs
                    e. None of these
Answer : c. Information

12. The machine cycle includes
                    a. fetch.                     b. decode
                    c. execute.                d. store
                    e. All of these
Answer : e. All of these

13. The word data is derived from
                      a. Greek.            b. English
                      c. Hindi.             d. Latin
                      e. Spanish
Answer : d. Latin


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