The simple interest on a certain sum of ₹P at a rate of r% per annum for 3 years is ₹11,250, and the compound interest on the same sum for 2 years at the same rate percent p.a. is ₹7,650. What are the values of P and r, respectively?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. ₹93750 and 4%.
SI = (P × R × T)/100
⇒ 11250 = (P × R × 3)/100
⇒ P = 375000/R .....(1)
CI for 2 years = P[(1 + R/100)2 - 1]
⇒ 7650 = P[(1 + R/100)2 - 1]
⇒ 7650 = (375000/R) × [ (1 + R/100)2 - 1 ]
⇒ (1 + R/100)2 - 1 = 7650 × R/375000
⇒ R/50 + R2/10000 = 0.0204R
⇒ R2 - 4R = 0
⇒ R = 4%
P = 375000/4 = 93750