Question

A and B lent a total of Rs.2787 at 15% compound interest, compounded annually. The amount A gets at the end of 3 years is same as B gets at the end of 5 years. Find the amount A lent. 
1. 1587
2. 1235
3. 1387
4. 1456

Answer 1

Correct Answer - Option 1 : 1587

Given

A and B lent Rs.2787 at 15% compound interest, compounded annually. The amount A gets at the end of 3 years is same as B gets at the end of 5 years

Concept used

Amount = Principal (1 + R/100)ⁿ

Calculation

Let A and B lent P and P' amount

As per the question

P + P' = 2787

P (1 + 3/20)³ = P'(1 + 3/20)⁵

\(\frac{P}{{P'}} = {\left( {1 + \frac{3}{{20}}} \right)^2}\)

\(\frac{P}{{P'}} = {\left( {\frac{{23}}{{20}}} \right)^2}\)

\(\frac{P}{{P'}} = \frac{{529}}{{400}}\)

529x + 400x = 2787

929x = 2787

x = 3

A lent 529 × 3 = Rs.1587