Question
Download Solution PDFA person invested a total sum of Rs. 9400 in three different schemes of simple interest at the annual rate of 9 percent, 12 percent and 15 percent. At the end of one year he got same interest in all three schemes. What is the sum invested at the rate of 12 percent?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Total investment = ₹9400
Rates = 9%, 12%, 15%
Time = 1 year
Same interest from each scheme
Formula used:
Simple Interest (SI) = (P × R × T) / 100
If interest is same, then P × R is constant for all
Let:
Amount at 9% = x, at 12% = y, at 15% = z
⇒ x + y + z = 9400
⇒ x × 9 = y × 12 = z × 15 = Same interest
So:
Let common interest = LCM of 9, 12, 15 = 180 units
Then, x = 180 / 9 = 20 units
y = 180 / 12 = 15 units
z = 180 / 15 = 12 units
Total units = 20 + 15 + 12 = 47 units
⇒ Value of 1 unit = 9400 / 47 = 200
⇒ y (at 12%) = 15 × 200 = 3000
∴ Amount invested at 12% = ₹3000
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