A sum is divided into three parts in the ratio 2 : 3 : 5. These parts are invested for 4 years at 5% p.a., 6% p.a., and 8% p.a. simple interest respectively. If the total simple interest earned from all three investments after 4 years is 6,800, find the total sum invested.
Show answer & explanation
Correct answer: B
Explanation
Given:
Ratio of parts = 2 : 3 : 5
Time = 4 years
Rate₁ = 5%, Rate₂ = 6%, Rate₃ = 8%
Total Simple Interest = ₹6800
According to the formula:
Simple Interest = (P × R × T) / 100
Let the total amount be 10x
First part = 2x
SI₁ = (2x × 5 × 4) / 100 = 0.4x
Second part = 3x
SI₂ = (3x × 6 × 4) / 100 = 0.72x
Third part = 5x
SI₃ = (5x × 8 × 4) / 100 = 1.6x
Total Interest = 0.4x + 0.72x + 1.6x = 2.72x
2.72x = 6800
x = 2500
Total Amount = 10x = 10 × 2500 = ₹25,000