A man invested a total of Rs. 12050 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 Rs.) invested at the compound interest is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 6000
Let the sum invested at compound interest be = a
⇒ Sum invested at simple interest = 12050 - a
According to the question;
(12050 - a) + (12050 - a) × 10/100 × 2 = a × (1 + 10/100)2
⇒ (12050 - a) [1 + 1/5] = a × 11/10 × 11/10
⇒ (12050 - a) × 6/5 = a × 121/100
⇒ 12050 × 6/5 - a × 6/5 = a × 121/100
⇒ 14460 = 121a/100 + 6a/5
⇒ 14460 = (121a + 120a)/100
⇒ 14460 = 241a/100
⇒ a = (14460 × 100)/241
⇒ a = 6000