Question

ram is as old as shyam will be when ram is twice as old as shyam was when ram's age was half the sum of their present age .and shyam is a s old as ram was when shyam was half the age he will be 10 years from now.
Find rams and Shyam’s present age.

Answer 1

Answer:

Shyam is 18.

We have 4 variables: Sn, St, Rn, Rt

(Shyan now, Shyan Then, Ram now, Ram Then)

Rn = 24 (Ram is now 24)

Rn = 2 St (Ram now is 2 times the age of Shyan then)

Rt = Sn (Ram then is the same age as Shyan now)

Rn - Rt = Sn - St (The same time has passed since now and then)

Then it is all just algebra.

St = Sn - Rn + Rt

St = 2Rt - Rn

Rn = 2 (2Rt - Rn)

Rn = 4Rt - 2Rn

3Rn = 4Rt

Rt = 3/4 Rn

Rn =24

Rt = 18

Rt = Sn = 18

Check:

Rn - Rt = 24 - 18 = 6

Sn - St = 18 - 1/2 Rn = 18 -12 = 6