A sum of Rs. 16800 is divided into two parts. One part is lent at a simple…
2022
A sum of Rs. 16800 is divided into two parts. One part is lent at a simple rate of interest of 6% per annum and the other part at 8% per annum. After 2 years the total sum received is Rs. 19,000. Find the sum lent at the rate of 6% and 8% respectively.
Answer: A. 12200, 4600 — CONCEPTFor simple interest, I = P × R × T / 100, and the final amount is A = P + I. When a total principal is split between two rates for the same time, write…
- A.
12200, 4600
- B.
11000, 5800
- C.
12000, 4800
- D.
4800, 12000
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Correct answer: A
CONCEPT
For simple interest, I = P × R × T / 100, and the final amount is A = P + I.
When a total principal is split between two rates for the same time, write one interest term for each part and add them to the known total interest.
APPLICATION
Let x be the amount lent at 6% per annum. Then 16800 − x is lent at 8% per annum.
The total interest received in two years is 19000 − 16800 = 2200.
Using simple interest for both parts: (x × 6 × 2 / 100) + ((16800 − x) × 8 × 2 / 100) = 2200.
Simplifying gives 0.12x + 0.16(16800 − x) = 2200, so 0.12x + 2688 − 0.16x = 2200.
Thus 0.04x = 488 and x = 12200. The other part is 16800 − 12200 = 4600.
CROSS-CHECK
Interest on 12200 at 6% for two years is 12200 × 6 × 2 / 100 = 1464.
Interest on 4600 at 8% for two years is 4600 × 8 × 2 / 100 = 736.
Their total interest is 1464 + 736 = 2200, so the final amount is 16800 + 2200 = 19000. Therefore, the amounts lent at 6% and 8% are 12200 and 4600, respectively.