If at same rate of interest, in 2 years, the simple interest is ₹42 and compound interest is ₹45, then what is the principal (in ₹)?
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Correct answer: B
Explanation
The correct answer is option 2 i.e. 147
Let principal = P and rate = R% per annum
SI for 2 years = P × R × 2 ÷ 100 = 42
P × R ÷ 100 = 21 → (Equation 1)
CI for 2 years = P × [(1 + R/100)² – 1] = 45
(1 + R/100)² – 1 = 45 ÷ P
But (1 + R/100)² – 1 ≈ 2(R/100) + (R/100)²
So 2(R/100) + (R/100)² = 45 ÷ P
From equation 1, R/100 = 21 ÷ P
Substitute: 2 × (21/P) + (21/P)² = 45 ÷ P
42/P + 441 / P² = 45 / P
441 / P² = 3 / P
P = 441 ÷ 3 = 147