Rohit invested \(\frac{1}{4}\) of a sum at 6% per annum, \(\frac{1}{3}\) of the sum at 8% per annum and the rest at 12% per annum, all at simple interest for 3 years. If the total interest received is Rs 6600, what is the total sum invested?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Rs 24000
Find what per cent of the whole sum the interest is: each part earns its own rate, and the shares add up.
Rest of the sum \(=1-\frac{1}{4}-\frac{1}{3}=\frac{5}{12}\)
Interest per year \(=\frac{1}{4}\times6+\frac{1}{3}\times8+\frac{5}{12}\times12=9\frac{1}{6}\%\) of the sum
For 3 years: \(9\frac{1}{6}\times3=27.5\%\) of the sum
Sum \(\displaystyle =\frac{6600\times100}{27.5}=24000\)
The total sum is Rs 24000.
Why the other options are incorrect
Option (2) Rs 20000 — Incorrect. On Rs 20000 the total interest would be Rs 5500, not Rs 6600.
Option (3) Rs 22000 — Incorrect. On Rs 22000 the total interest would be Rs 6050, not Rs 6600.
Option (4) Rs 26400 — Incorrect. On Rs 26400 the total interest would be Rs 7260, not Rs 6600.