What will be the share of R in the profit earned by V, R and A together? I. They together invested an amount of ` 54000 for a period of 1 year. II. R’s investment was 25% less than V’s and 50% more than A’s. III. The profit of V is ` 4000 more than that of A.
(a)Only I and II together
(b)Only II
(c)Only II and III together
(d)II and either I or III only
Answer
Answer (as printed): C
Explanation
From II and III, we have: let A's investment $=₹x$. Then, R's investment $=150\%$ of ₹$x=₹\left(\frac{3x}{2}\right)$. Now, $75\%$ of V's investment $=\frac{3x}{2} \Rightarrow$ V's investment $=\left(\frac{3x}{2}\times\frac{100}{75}\right)=₹2x$. $V:R:A=2x:\frac{3x}{2}:x=4:3:2$. Let the total profit be ₹$P$. Then, V's share $=₹\left(\frac{4P}{9}\right)$ and A's share $=₹\left(\frac{2P}{9}\right)$. So, $\frac{4P}{9}-\frac{2P}{9}=4000 \Rightarrow P=\left(\frac{4000\times9}{2}\right)=18000$. R's share $=₹\left(18000\times\frac{3}{9}\right)=₹6000$. Thus, both II and III together give the answer. $\therefore$ Correct answer is (c).
Explanation as extracted from the printed page; notation may be imperfect.