Rs 2,400 is invested in two parts. The first part earns simple interest at 8% per annum and the second part at 5% per annum. If the total interest at the end of one year is Rs 165, find the sum invested at 5%.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Rs 900
The average rate is \(165\div2400\times100=6.875\%\); by alligation, the two parts are in the ratio of the distances of the rates from this average.
Average rate \(=6.875\%\)
First part : second part \(=(6.875-5):(8-6.875)=5:3\)
Second part \(\displaystyle =\frac{3}{8}\times2400=900\)
The sum invested at 5% is Rs 900.
Why the other options are incorrect
Option (2) Rs 600 — Incorrect. With Rs 600 at 5% and Rs 1,800 at 8%, the interest is Rs 174, not Rs 165.
Option (3) Rs 1,500 — Incorrect. With Rs 1,500 at 5% and Rs 900 at 8%, the interest is Rs 147, not Rs 165.
Option (4) Rs 1,200 — Incorrect. With Rs 1,200 at 5% and Rs 1,200 at 8%, the interest is Rs 156, not Rs 165.