The ratio of the interest received when Rs. (x + 500) is invested at 32% p.a. simple interest for 4 years to the interest received when Rs. (x - 500) is invested at 20% p.a. compound interest, compounded annually for 2 years, is 64:11. Find the value of 'x'.
Show answer & explanation
Correct answer: B
Explanation
Given:
First investment = (x + 500), time = 4 years, rate = 32% (simple interest)
Second investment = (x − 500), time = 2 years, rate = 20% (compound interest)
Interest ratio = 64 : 11
By formula:
Simple interest = (P × R × T) / 100
Compound interest (2 years) = P[(1 + R/100)² − 1]
Interest on first investment = (x + 500) × 32 × 4 / 100 = 1.28(x + 500)
Interest on second investment = (x − 500)[(1.2)² − 1] = 0.44(x − 500)
1.28(x + 500) : 0.44(x − 500) = 64 : 11
1.28(x + 500) / 0.44(x − 500) = 64 / 11
(32/11) × (x + 500)/(x − 500) = 64/11
(x + 500)/(x − 500) = 2
x + 500 = 2x − 1000
x = 1500