Four year ago, Shyam's age was 3/4 times of that of Ram. Four year hence, Shyam's age will be 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 :
\[4\,\,yr\]ago, let Ram's age \[=\,\,x\,\,yr\]and |
Shyam's age \[=\frac{3}{4}x\,\,yr\] |
Now, Ram's present age \[(x+4)\,\,yr\] |
and Shyam's present age \[=\left( \frac{3}{4}x+4 \right)yr\] |
According to the question, |
\[\frac{5}{6}(x+4+4)=\left( \frac{3}{4}x+4+4 \right)\] |
\[\Rightarrow \] \[4\,\,(5x+40)=6\,\,(3x+32)\] |
\[\Rightarrow \] \[20x+160=18x+192\]\[\Rightarrow \]\[2x=32\] |
\[\therefore \] \[x=16\] |
Hence, present age of Shyam\[=\frac{3}{4}\times 16+4=16\,\,yr\] |
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