If the rate increases by 2\%, the simple interest received on a sum of money increases by ₹ 108. If the time period is increased by 2 years, the simple interest on the same sum increases by ₹ 180 . The sum is:
(a)₹ 1800
(b)₹ 3600
(c)₹ 5400
(d)Data inadequate
(e)None of these
Answer
Answer (as printed): D
Explanation
Let the sum be ₹ $x$, rate be $R \%$ p.a. and time be $T$ years. Then, $\left[\frac{x \times(R+2) \times T}{100}\right]-\left(\frac{x \times R \times T}{100}\right)=108$ $$\begin{aligned} & \Leftrightarrow \quad 2 x T=10800 \\ & \text { And, }\left[\frac{x \times R \times(T+2)}{100}\right]-\left(\frac{x \times R \times T}{100}\right)=180 \\ & \Leftrightarrow \quad 2 x R=18000 \end{aligned}$$ Clearly, from (i) and (ii), we cannot find the value of $x$. So, the data is inadequate.
Explanation as extracted from the printed page; notation may be imperfect.