Question

Aman invested Rs. (P + 3000) for 3 years at 8% simple interest. Anuj invested an amount of Rs. P for 2 years at 12% compound interest and received the same amount of interest as Aman received. Find the amount that is invested by Anuj.

• A. Rs. 45,000
• B. Rs. 50,000
• C. Rs. 55,000
• D. Rs. 60,000

Answer 1

The Correct Option is B

Aman and Anuj received the same amount of interest from their respective investments. Let's calculate the amount each of them received:

Aman's Investment:

Principal: Rs. (P + 3000)

Rate of simple interest: 8% per annum

Time: 3 years

Simple Interest formula: \[SI = \frac{P \times R \times T}{100}\]

\[SI = \frac{(P+3000) \times 8 \times 3}{100}\]

\[SI = \frac{24(P+3000)}{100}\]

\[SI = 0.24(P+3000)\]

Anuj's Investment:

Principal: Rs. P

Rate of compound interest: 12% per annum

Time: 2 years

Compound Interest formula: \[A = P \left(1 + \frac{R}{100}\right)^T\]

\[A = P \left(1 + \frac{12}{100}\right)^2\]

\[A = P \left(\frac{112}{100}\right)^2\]

\[A = P \times \frac{12544}{10000}\]

\[A = P \times 1.2544\]

Compound Interest, \[CI = A - P\]

\[CI = P \times 1.2544 - P\]

\[CI = 0.2544 \times P\]

Equating both interests:

\[0.24(P + 3000) = 0.2544P\]

Solving for P:

\[0.24P + 720 = 0.2544P\]

\[720 = 0.2544P - 0.24P\]

\[720 = 0.0144P\]

\[P = \frac{720}{0.0144}\]

\[P = 50000\]

Therefore, Anuj invested Rs. 50,000.