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Question
In how much time will the simple interest on ₹ 3,000 at the rate of 8% per annum be the same as simple interest on ₹ 4,000 at 12% per annum for 4 years?
Solution
Let the required number of years be x
Simple Interest I = `"Pnr"/100`
Principal P1 = ₹ 3000
Rate of interest (r) = 8%
Time (n1) = n1 years
Simple Interest I1 = `(3000 xx 8 xx "n"_1)/100` = 240 n1
Principal (P2) = ₹ 4000
Rate of interest (r) = 12%
Time n2 = 4 years
Simple Interest I2 = `(4000 xx 12 xx 4)/100`
I2 = 1920
If I1 = I2
240 n1 = 1920
n1 = `1920/240`
= 8
∴ The required time = 8 years
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