What is the principal sum? (SNAP, 2005) I. The interest amount after 30 months is half the interest amount after 5 years. II. The sum amounts to ` 1050 in 5 years at simple interest rate. III. The rate of interest is 8% p.a.
(a)I and II only
(b)II and III only
(c)I and III only
(d)I and III only, or II and III only SIMPLE INTEREST
Answer
Answer (as printed): B
Explanation
Let the sum be ₹ $x$ Clearly, the fact given in I always hold true, irrespective of the sum. So, I does not give us the answer. From II and III, we have: $A=₹ 750, T=5 \mathrm{yrs}, R=8 \%$. $$\begin{aligned} & \therefore \quad x+\frac{x \times 8 \times 5}{100}=1050 \Rightarrow x+\frac{2 x}{5}=1050 \Rightarrow \frac{7 x}{5}=1050 \\ & \Rightarrow \quad x=\left(\frac{1050 \times 5}{7}\right)=750 . \end{aligned}$$ Thus, II and III together give the answer. ∴ Correct answer is (b).
Explanation as extracted from the printed page; notation may be imperfect.