Correct Answer - Option 3 : Rs. 16,000/-
Given:
A person takes a some amount on loan at 3% per annum simple interest payable annually.
He gives it on loan at 5% per annum compound interest payable half yearly.
At the end of year he earns profit of Rs. 330/-
Concept used :
If the compound interest rate is '2x'% per annum payable half yearly, then
Total interest after a year
= [x + x + (x × x)100]%
Calculations :
Let the amount taken in loan be Rs. '100x'
Total interest he have to pay
⇒ 100x + 3% of 100x
⇒ 103x
Total interest he got = (5/2) + (5/2) + (5 × 5)/400]%
⇒ (81/16)%
Total interest he got = 100x + (81/16)% of 100x
⇒ 100x + (81/16)x
⇒ (1681/16) x
Profit = (1681/16)x - 103x
⇒ 330 = (33/16)x
⇒ x = 160
Total loan he took = 100x
⇒ 100 x
⇒ 100 × 160
⇒ 16000 Rupees
∴ Correct choice will be option 3.
