 # Question

Last.year peter was.five times as old as his son roy..given that their total ages now are 38 years. How old will peter be when he is thrice as.old as his son ?

This is a Before After question.

 Before Transfer After now Peter 5u +1 5u + 1 31 Son 1u +1 1u + 1 7 Total 6u 6u + 2

6u + 2 = 38

6u = 38 – 2 = 36

1u = 36 ÷ 6 = 6

6 + 1 = 7

5u = 5 × 6 = 30

30 + 1 = 31

7 + 5 = 12

31 + 5 = 36

Last two steps 7 + 5 can you exp ?

I simplified it by using trial and error method.

Now       7           31

1 year    8           32

2 years   9           33

3 years   10         34

4 years     11      35

5 years      12         36

Alternatively,  you may use the cross multiplcation method.

(7 + 1u)/1  = (31 + 1u)/3

21 + 3u = 31 + 1u

3u – 1u = 31 – 21

2u = 10

1u = 10 ÷ 2 = 5

Alternatively,  you may use the Difference method.

31 – 7 = 24

2u = 24

1u = 24 ÷ 2 = 12

12 – 7 = 5 years

31 + 5 = 36 years old

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Last year —
Peter : 5 units
Roy : 1 unit

5 + 1 + 6
6 units + 2 = 38
1 unit = (38 – 2)/6 = 6
5 units = 30

Now —
Peter : 31
Roy : 7

7 x 3 = 21
31 – 21 = 10
10/2 = 5
5 + 31 = 36

Ans : 36 years old.

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Last Yr          Now              ? Yrs later

P          5u                 5u + 1              3p

R           u                    u + 1              p

5u+1+u+1 = 38

6u = 38 – 2

= 36

1u = 36÷6

= 6

Difference btw P and R = 4u

= 24

2p = 24

1p = 12

Peter’s age = 3p

= 3 × 12

= 36 (ans)