Q.A certain sum of money amounts to ₹944 in 3 years at simple interest. If the rate of interest is increased by 25%, the same sum amounts to ₹980 in the same time period. Find the principal amount and the original rate of interest.

Let the total amount of money be \(x\) rupees and the rate of interest be \(y\%\). So, using the simple interest formula: \[ x + \frac{x \times 3 \times y}{100} = 944 \] Multiplying through by 100: \[ 100x + 3xy = 94400 \Rightarrow 3xy = 94400 - 100x \Rightarrow xy = \frac{94400 - 100x}{3} \quad \text{—— (i)} \] Now, if the rate of interest is increased by 25%, the new rate becomes: \[ y + \frac{25y}{100} = \frac{5y}{4} \] So, the new amount becomes: \[ x + \frac{x \times 3 \times \frac{5y}{4}}{100} = 980 \Rightarrow x + \frac{15xy}{400} = 980 \Rightarrow x + \frac{3xy}{80} = 980 \Rightarrow 80x + 3xy = 78400 \Rightarrow 3xy = 78400 - 80x \Rightarrow xy = \frac{78400 - 80x}{3} \quad \text{—— (ii)} \] Equating equations (i) and (ii): \[ \frac{94400 - 100x}{3} = \frac{78400 - 80x}{3} \Rightarrow 94400 - 100x = 78400 - 80x \Rightarrow -20x = -16000 \Rightarrow x = 800 \] Now substituting \(x = 800\) into equation (i): \[ 800y = \frac{94400 - 80000}{3} = \frac{14400}{3} \Rightarrow y = \frac{14400}{3 \times 800} = 6 \] ∴ The principal amount is ₹80% and the rate of interest is 6%
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