Peter gave one-fourth of the amount he had to Michael. Michael in turn gave half of what he received from Peter to Sam. If the difference between the remaining amount with Peter and the amount received by Sam is ₹ 500, how much money did Michael receive from Peter?
(a)₹ 100
(b)₹ 200
(c)₹ 400
(d)Data inadequate
(e)None of these
Answer
Answer (as printed): B
Explanation
Suppose initially Peter had ₹ $x$. Then, Amount received by Michael $=₹\left(\frac{x}{4}\right)$. Amount remain- $$\text { ing with Peter }=₹\left(x-\frac{x}{4}\right)=₹\left(\frac{3 x}{4}\right) .$$ Amount received by Sam $=₹\left(\frac{1}{2} \times \frac{x}{4}\right)=₹\left(\frac{x}{8}\right)$. $$\therefore \quad \frac{3 x}{4}-\frac{x}{8}=500 \Leftrightarrow 5 x=4000 \Leftrightarrow x=800 .$$ Hence, amount received by Michael $=(x / 4)=₹ 200$.
Explanation as extracted from the printed page; notation may be imperfect.