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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