One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has ₹ 1,50,000 as total savings, how much has he saved in Public Provident Fund?
(a)₹ 30,000
(b)₹ 50,000
(c)₹ 60,000
(d)₹ 90,000
Answer
Answer (as printed): C
Explanation
Let savings in N.S.C. and P.P.F. be ₹ $x$ and ₹ $(150000-x)$ respectively. Then, $$\begin{aligned} \frac{1}{3} x=\frac{1}{2}(150000-x) & \Leftrightarrow \frac{x}{3}+\frac{x}{2}=75000 \\ & \Leftrightarrow \frac{5 x}{6}=75000 \\ & \Leftrightarrow x=\left(\frac{75000 \times 6}{5}\right)=90000 . \end{aligned} \begin{aligned} \therefore \text { Savings in Public Provident Fund } & =₹(150000-90000) \\ & =₹ 60000 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.