A sum is divided into three parts in the ratio 3 : 4 : 5. The first part is invested at 6% p.a. simple interest for 2 years, the second at 8% p.a. for 3 years, and the third at 10% p.a. for 4 years. If the total simple interest received from the three parts after their respective periods is 8,300, find the total sum invested.
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Correct answer: D
Explanation
Given:
Ratio = 3 : 4 : 5
Rate₁ = 6%, Time₁ = 2 years
Rate₂ = 8%, Time₂ = 3 years
Rate₃ = 10%, Time₃ = 4 years
Total Simple Interest = 8300
According to the formula:
Simple Interest = (P × R × T) / 100
Let the amounts be = 3x, 4x, 5x
Interest on the first part = (3x × 6 × 2)/100 = 36x/100
Interest on the second part = (4x × 8 × 3)/100 = 96x/100
Interest on the third part = (5x × 10 × 4)/100 = 200x/100
Total Interest:
(36x + 96x + 200x)/100 = 8300
332x/100 = 8300
332x = 830000
x = 2500
Total Amount = 3x + 4x + 5x = 12x = 12 × 2500 = 30,000 Rupees