Question

If the simple interest on the certain sum of money for 15 months at 7 1/2% per annum exceeds the simple interest on the same sum for 8 months at 12 1/2% per annum by rs. 32.50, then the sum of money (in rs.) is

Answer 1

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Answer 2

Answer:

Rs.3120

Step-by-step explanation:

Let the principal be x

Case 1:

Principal = x

Time = 15 months = $\frac{15}{12} year$

Rate of interest=$7\frac{1}{2}=\frac{15}{2}\%$

Simple interest = $\frac{Principal \times Rate \times Time }{100}$

Simple interest = $\frac{x \times 15 \times 15 }{2 \times 12 \times 100}$

Simple interest = $\frac{3x}{32}$

Case 2:

Principal = x

Time = 8 months = $\frac{8}{12} year$

Rate of interest=$12\frac{1}{2}=\frac{25}{2}\%$

Simple interest = $\frac{Principal \times Rate \times Time }{100}$

Simple interest = $\frac{x \times 25 \times 8 }{2 \times 12 \times 100}$

Simple interest = $\frac{x}{12}$

The simple interest on the certain sum of money for 15 months at 7 1/2% per annum exceeds the simple interest on the same sum for 8 months at 12 1/2% per annum by rs. 32.50

So, $\frac{3x}{12}-\frac{x}{12}=32.50$

$\frac{x}{96}=32.50$

$x=3120$

Hence the sum of money (in rs.) is 3120