Simple Interest and compound interest (corresponding annually) on a principal at a certain rate of interest for 2 years are Rs. 12000 and Rs. 14400 respectively. What is the principal?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. Rs. 15000.
We know that,
S.I. = (P × R × T) and,
C.I. = P(1 + R/100)T - P
here, S.I. = Simple Interest, C.I. = Compund Interest, P = Principal, R = Rate%, T= Time,
⇒ S.I. = (P × R × T)
⇒ 12000 = (P × R × 2)
⇒ P × R = 6000
⇒ R = 6000/P.......(1)
Now,
⇒ C.I. = P(1 + R/100)T - P
⇒ 14400 = P(1 + R)2 - P
⇒ 14400 = P((1 + R)2 - 1)
⇒ 14400 = P(1 + R2 + 2R - 1)
⇒ 14400 = P(R2 + 2R)
⇒ 14400 = P(R(R + 2)....(2)
Putting eq 1 in 2
⇒ 14400 = P((6000/P)2 + 2 × (6000/P))
⇒ 14400 = P(36000000/P2 + 12000/P)
⇒ 14400 = 36000000/P + 12000
⇒ 14400 - 12000 = 36000000/P
⇒ 2400 = 36000000/P
⇒ P = 36000000/2400
⇒ P = Rs.15000
Therefore, the principal amount is Rs. 15000