Question
A man invests a sum of ₹3600 at a simple interest
rate of r% per annum for x years. His friend invests ₹4000 at the same rate of interest r% per annum for (x + 4) years. The simple interest earned by the first man is 0.45 times the simple interest earned by his friend.Solution
ATQ, Let rate = r% per annum. Interest of first man (A): I ₁ = 3600 × r × x / 100 Interest of second man (B): I ₂ = 4000 × r × (x + 4) / 100 Given: I ₁ = 0.45 × I ₂ 3600 × r × x / 100 = 0.45 × 4000 × r × (x + 4) / 100 Cancel r and 100 from both sides: 3600x = 0.45 × 4000 × (x + 4) 0.45 × 4000 = 1800 So, 3600x = 1800(x + 4) 3600x = 1800x + 7200 3600x − 1800x = 7200 1800x = 7200 x = 7200 ÷ 1800 = 4
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