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InterviewSolution
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A certain sum amounts to ₹ 756 in 2 years and to ₹ 873 is \(3\frac{1}{2}\) years at a certain rate of simple interest. The rate of interest per annum is:1. 11%2. 13%3. 10%4. 12% |
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Answer» Correct Answer - Option 2 : 13% Given: First Amount = Rs. 756 Time = 2 years Second Amount = Rs. 873 Time = \(3\frac{1}{2}\) years = 7/2 years Formula Used: Simple Interest = Amount – Principal Simple Interest = (Principal × Rate × time)/100 Calculation: Let the principal be 'x'. Simple Interest = Amount - Principal ⇒ 756 – x Simple Interest = (Principal × Rate × time)/100 Rate = (S.I × 100)/ P × t ⇒ Rate = ((756 – x) × 100)/ (x × 2) Simple Interest = Amount - Principal ⇒ 873 – x Rate = ((873 – x) × 100)/ (x × 7/2) According to the Question, ((756 – x) × 100)/ (x × 2) = ((873 – x) × 100)/ (x × 7/2) ⇒ ((756 – x) × 100)/2 = 2((873 –- x) × 100)/ 7 ⇒ 7((756 – x) × 100)= 4((873 – x) × 100) ⇒ 529200 – 700x = 349200 – 400x ⇒ 300x = 180000 ⇒ x = 600 Rate = ((756 – x) × 100)/ (x × 2) ⇒ ((756 – 600) × 100)/(600 × 2) ⇒ (156 × 100)/ 1200 ⇒ 13% ∴ The rate of interest per annum is 13%.
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