Question

the simple interest on a certain sum for 3 years at 8% per annum is rupees 96 more than the simple interest on the same sum for 2 years at 9% per annum find the sum . (answer is 1600)

Answer 1

et the required sum be rs.x

SI on Rs.x at 8%per annum for 3 years

=Rs.(x×8×3/100)=Rs.6x/25

Si on rs.x at 9%per annum for 2 years

=Rs.(x×9×2/100)=Rs.9x/50

6x/25-9x/50=96

=>12x-9x=96×50

=>3x=96×50

=>x=96×50/3=1600

hence the required sumis Rs.1600

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Answer 2

$\huge\mathfrak\red{Question:}$

The simple interest on a certain sum for 3 years at 8% per annum is Rs. 96 more than the simple interest on the same sum for 2 years at 9% per annum. Find the sum.

$\huge\mathfrak\green{Solution:}$

Let the required sum be Rs. x. Then,

SI on Rs. x at 8% p.a. for 3 years

$= rs.( \frac{x \times 8 \times 3}{100} ) = rs .\:\frac{6x}{25}$

SI on Rs. x at 9% p.a. for 2 years

$rs.( \frac{x \times 9 \times 2}{100} ) = rs. \frac{9x}{50}$

Hence,

$\frac{6x}{25} - \frac{9x}{50} = 96$

$(12x - 9x) = 96 \times 50$

$3x = 4800$

$x = \frac{4800}{3}$

$x = 1600$

Hence, the required sum is Rs. 1600