question_answer

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?

A) 15 yr                

B) 20 yr

C) 16 yr    

D) 24 yr

E) 8 yr

Correct Answer: C

Solution :

Let Ram's present age \[=x\,\,yr\]

and Shyam's present age \[=y\,\,yr\]

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 \[=16\,\,yr\]