Peter lent some amount of money at 5% simple interest and anequal amount of money at 7% simple interest, each for 3 years. If totalinterest earned on both the sum was Rs 360, what amount was lent in each case?Rs 2000Rs 3600Rs 2500Rs 1000
Question
Peter lent some amount of money at 5% simple interest and anequal amount of money at 7% simple interest, each for 3 years. If totalinterest earned on both the sum was Rs 360, what amount was lent in each case?Rs 2000Rs 3600Rs 2500Rs 1000
Solution
Let's solve this step by step:
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Let's assume the amount of money lent in each case is Rs x.
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The total interest earned from both the sums is the sum of the interest earned from each sum.
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The formula for simple interest is I = PRT/100, where P is the principal amount (the amount lent), R is the rate of interest, and T is the time in years.
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So, the interest earned from the first sum is (x53)/100 and from the second sum is (x73)/100.
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According to the problem, the total interest earned from both the sums is Rs 360. So, we can set up the equation: (x53)/100 + (x73)/100 = 360.
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Simplifying the equation gives: (15x + 21x)/100 = 360, which further simplifies to 36x/100 = 360.
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Solving for x gives x = (360*100)/36 = Rs 1000.
So, the amount of money lent in each case was Rs 1000.
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