A person invested a sum of money. The value of the investment increased by 12% in the first year and by 9% in the second year. If the value of the investment after two years was Rs 97664, what is half of the sum invested?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs 40000
Each year’s increase is worked out on the value at the start of that year, so the sum is multiplied by 1.12 in the first year and then by 1.09 in the second year.
Let the sum be Rs \(P\); value after two years \(=P\times1.12\times1.09=1.2208P\)
\(1.2208P=97664\)
\(\displaystyle P=\frac{97664}{1.2208}=80000\)
Half of the sum \(=80000\div2=40000\)
Half of the sum invested is Rs 40000. (Rs 80000, Option (1), is the whole sum.)