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Question
The simple interest on a certain sum for 2.5 years at 12 per cent per annum is ₹ 300 less than the simple interest on the same sum for 4.5 years at 8 per cent per annum. Find the sum.
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Solution
Let the sum be ₹ P.
Interest for 2.5 years at 12% per annum
= `(P xx 12 xx 2.5)/100`
= `3/10 P`
Interest for 4.5 years at 8% per annum
= `P xx 8/100 xx 4.5`
= `9/25 P`
According to question,
`3/10 P = 9/25 P - 300`
⇒ `(9/25 - 3/10) P = 300`
⇒ `((36 - 30))/100 P = 300`
⇒ `6/100 P = 300`
⇒ `P = (300 xx 100)/6 = 5000`
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Simple interest on a given amount is always less than or equal to the compound interest on the same amount for the same time period and at the same rate of interest per annum.
The simple interest on a sum of ₹ P for T years at R% per annum is given by the formula: Simple Interest = `(T xx P xx R)/100`.
