If at same rate of interest, in 2 years, the simple interest is ₹40 and compound interest is ₹50, then what is the principal (in ₹)?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 40 .
Let principal = P and rate = R% per annum
Simple interest for 2 years = P × R × 2 ÷ 100 = 40
P × R = 2000 …(1)
Compound interest for 2 years = P × [(1 + R/100)2 − 1] = 50
(1 + R/100)2 − 1 = 50 ÷ P …(2)
From (1)→ R = 2000 ÷ P
Substitute in (2),
(1 + 2000 ÷ (100 × P))2 − 1 = 50 ÷ P
(1 + 20 ÷ P)2 − 1 = 50 ÷ P
1 + 40/P + 400/P2 − 1 = 50/P
40/P + 400/P2 = 50/P
400/P2 = 10/P → 400 = 10 × P → P = 40