A man invested a total of ₹12,050 in two parts, one at 10% p.a. simple interest for 2 years and the other at the same rate at compound interest, interest being compounded annually, for the same time. The amounts he received from both the parts are equal. The sum(in ₹) invested at the compound interest is:

6,000

Formula used here is :-

Simple Interest = \(\frac{P ×R ×T}{100}\)

Compound interest = P(1+$\frac{R}{100})^t$– P  

Let amount invested on SI = x & Amount invested on CI = y

x + \(\frac{x ×2 ×10}{100}\) = y × \(\frac{11}{10}\) × \(\frac{11}{10}\)

x + \(\frac{x}{5}\) = y × \(\frac{121}{100}\)

\(\frac{6x}{5}\) =  \(\frac{121y}{100}\)

\(\frac{x}{y}\) =  \(\frac{121}{120}\)

ATQ,

( 121 + 120 )units = 12050

1 unit = 50

So, Amount invested on CI = 120 × 50 = Rs. 6000