The simple interest on a sum of money for years at 10% per annum is Rs. 30 more than the simple interest on the same for 1 year at 12% per annum. Find the principal amount.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. ₹1,000.
Let the sum of money be P
We know that,
S.I. = (P × R × T)/100
here, S.I. = Simple Interest, P = principal, R = Rate, and T = Time
The simple interest for 3/2 years at 10% per annum
⇒ SI1 = (P × 10 × 3/2)/100
⇒ SI1 = 15P/100
⇒ SI1 = 0.15P
The simple interest for 1 year at 12% per annum
⇒ SI2 = (P × 12 × 1)/100
⇒ SI2 = 12P/100
⇒ SI2 = 0.12P
It is given that the simple interest for 3/2 years at 10% per annum is Rs. 30 more than the simple interest for 1 year at 12% per annum.
Therefore,
⇒ SI1 = SI2 + 30
On putting the values of SI1 and SI2
⇒ 0.15P = 0.12P + 30
⇒ 0.15P - 0.12 = 30
⇒ 0.03P = 30
⇒ P = 30/0.03
⇒ P = 1000
Thus, the sum of money is Rs. 1,000.