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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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