A man invested ₹ 5000 at some rate of simple interest and ₹ 4000 at 1 percent higher rate of interest. If the interest in both the cases after 4 years is same, the rate of interest in the former case is
(a)4\% p.a.
(b)5\% p.a.
(c)$6 \frac{1}{4} \%$ p.a.
(d)$8 \frac{1}{3} \%$ p.a.
Answer
Answer (as printed): A
Explanation
Let the rates of interest in the former and latter cases be $R \%$ and $(R+1) \%$ p.a. Then, $5000 \times R \times 4=4000 \times(R+1) \times 4$ $$\Rightarrow \quad \frac{R+1}{R}=\frac{5000 \times 4}{4000 \times 4} \Rightarrow 1+\frac{1}{R}=1+\frac{1}{4} \Rightarrow R=4 .$$ Hence, required rate $=4 \%$ p.a.
Explanation as extracted from the printed page; notation may be imperfect.