Question

Avinash invested an amount of ₹ 10,000 divided in two different schemes giving a return of 5 % p.a and 15 % p.a. If the interest received in both the schemes is same after a period of 2 years.Find the sum invested at the rate of 5 % p.a.

• A. ₹ 7,500
• B. ₹ 5,500
• C. ₹ 4,000
• D. ₹ 6,000

Answer 1

The correct option is A ₹ 7,500

Let the sum invested at the rate of 5 % p.a be ₹ x.
Hence, the sum invested at the rate of 15 % p.a = ₹ (10,000-x).

The Simple Interest earned on a sum of ₹ P for a period of T years at the rate of R % p.a S.I is given by $\frac{P\times R\times T}{100}$.

Since, both of schemes receive the same interest after 2 years,

$\frac{x\times 5\times 2}{100}$ = $\frac{(10,000-x)\times 15\times 2}{100}$

$\frac{10x}{100}=\frac{(10,000-x)30}{100}$
$10x=10,000\times 30-30x$
$40x=10,000\times 30$

$\Rightarrow x=₹7,500$

Hence, the amount invested at the rate of 5 % p.a = ₹ 7,500.