Simple interest and compound interest on a principal at a certain rate of interest for 2 years is Rs. 12800 and Rs. 14400 respectively. What is the principle?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. Rs. 25600.
S.I. = (P × R × T)/100
here, S.I. = Simple Interest, P = Principle, R = Rate, and T = Time
⇒ 12800 = (P × R × 2)/100
⇒ 12800 = 2PR/100
⇒ 1280000 = 2PR
⇒ PR = 640000
Now,
⇒ C.I. = P(1 + R/100)T - P
Here, C.I. = Compound Interest, P = Principal, R = Rate, and T = Time
⇒ 14400 = P(1 + R/100)2 - P
⇒ 14400 = P[(1 + R/100)2 - 1]
⇒ 14400 = P[R2/10000 + 2R/100]
⇒ 14400 = P(R2 + 200R)/10000
⇒ 14400 × 1000 = P(R2 + 200R)
⇒ P(R2 + 200R) = 14400000
On putting P = 640000/R from eq(1)
⇒ (640000 × (R2 + 200R)/R) = 144000000
⇒ 640000R2 + 128000000R = 144000000R
⇒ 640000R2 = 16000000R
⇒ R2 = 25R
⇒ R = 25
Putting the value of R in equation(1)
⇒ PR = 640000
⇒ P × 25 = 640000
⇒ P = 640000/25
⇒ P = Rs.25600
Hence, the principal is Rs.25600