A total sum of 30,000 is divided into two parts. One part is invested at 7% p.a. simple interest and the other at 11% p.a. simple interest. After 5 years, the total simple interest from both parts is 12,000. Find the amounts invested at 7% and 11% respectively.
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Correct answer: C
Explanation
Given:
Total Amount = 30,000
Time = 5 years
Rate₁ = 7%, Rate₂ = 11%
Total Simple Interest = 12,000
According to the formula:
Simple Interest = (P × R × T) / 100
Let the amount at 7% be = x ⇒ Amount at 11% = (30,000 − x)
Total Interest:
( x × 7 × 5 )/100 + ((30,000 − x) × 11 × 5)/100 = 12,000
35x/100 + 55(30,000 − x)/100 = 12,000
35x + 55(30,000 − x) = 1,200,000
35x + 1,650,000 − 55x = 1,200,000
−20x = −450,000
x = 22,500
At 7% = 22,500
At 11% = 30,000 − 22,500 = 7,500
At 7% = ₹22,500, At 11% = ₹7,500