Question

The ratio of ages of ramesh and suresh 5 years from now will be 2 : 5 and the ratio of the ages of mahesh and suresh 15 years before was 3 : 2. What is the average of their present ages if the mahesh was 45 years old when ramesh was born?

Answer 1

Let the ages of Ramesh, Suresh and Mahesh be represented by R, S, M respectively.
Now, given M=R+45

(R+5)/(S+5) = 2/5
=> 5R + 25= 3S +1 0
=> 3S - 5R = 15 --------------(1)

Also,

(M-15)/(S-15) = 3/2
Putting M= R+45,
=> (R+30)/(S-15)= 3/2
=> 2R + 60= 3S - 45
=> 3S-2R = 105 ------------------(2)

Subtracting (1) from (2),

3S - 2R = 105
-(3S - 5R = 15)
----------------------------
3R = 90
=> R= 30.

Therefore,
M=R+45
M= 30 + 45= 75.

3S - 2R = 105
=> 3S - 60= 105
=> 3S = 45
=> S = 15.

Therefore, average of present ages
=(75+15+30)/3
=40. _______________Ans.