Sunita invested \(\frac{1}{5}\) of a sum at 5% per annum, \(\frac{1}{2}\) of the sum at 7% per annum and the rest at 10% per annum, all at simple interest for 2 years. If the total interest received is Rs 5400, what is the total sum invested?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs 36000
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 \(=1-\frac{1}{5}-\frac{1}{2}=\frac{3}{10}\)
Interest per year \(=\frac{1}{5}\times5+\frac{1}{2}\times7+\frac{3}{10}\times10=7.5\%\) of the sum
For 2 years: \(7.5\times2=15\%\) of the sum
Sum \(\displaystyle =\frac{5400\times100}{15}=36000\)
The total sum is Rs 36000.
Why the other options are incorrect
Option (1) Rs 32400 — Incorrect. On Rs 32400 the total interest would be Rs 4860, not Rs 5400.
Option (3) Rs 30000 — Incorrect. On Rs 30000 the total interest would be Rs 4500, not Rs 5400.
Option (4) Rs 40000 — Incorrect. On Rs 40000 the total interest would be Rs 6000, not Rs 5400.