Quantitative Aptitude Ques 988

Question: Four years ago Shyam’s age was $ \frac{3}{4} $ times that of Ram. Four years hence, Shyam’s age will be $ \frac{5}{6} $ times that of Ram. What is the present age of Shyam?

Options:

A) 15 yr

B) 20 yr

C) 16 yr

D) 24 yr

E) 8 yr

Show Answer

Answer:

Correct Answer: C

Solution:

  • Let Ram’s present age $ =xyr $ and Shyam’s present age $ =yyr $
    According to the question $ y-4=\frac{3}{4}(x-4) $

$ \Rightarrow $ $ 4y-16=3x-12 $

$ \Rightarrow $ $ 3x-4y=-4 $ … (i) and $ y+4=\frac{5}{6}(x+4) $

$ \Rightarrow $ $ 6y+24=5x+20 $

$ \Rightarrow $ $ 6y-5x=-4 $ … (ii) On solving Eqs. (i) and (ii), we get

$ \Rightarrow $ $ -2y=-32 $

$ \Rightarrow $ $ y=16 $

$ \therefore $ Shyam’s present age $ =16yr $