Question

6. Find the sum on which the difference between
the simple interest and the compound interest
at the rate of 8% per annum compounded annually be Red 64 in 2 yeaes​

Answer 1

${ \bold{ \huge{ \underline{ \blue{Question:-}}}}}$

Find the sum on which the difference between the simple interest and the compound interest at the rate of 8% per annum compounded annually be Rs. 64 in 2 years

${ \bold{ \huge{ \underline{ \blue{Solution:-}}}}}$

${ \bold{ \red{GIVEN -}}}$

• Difference between simple interest and compound interest = Rs. 64

• Rate = R = 8%

• Time = T = 2 years

${ \bold{ \red{</strong><strong>TO</strong><strong> </strong><strong>FI</strong><strong>ND</strong><strong> </strong><strong>-</strong><strong>}}}$

• Principal???

Let the sum ( principal ) be Rs. x

${ \bold{ \underline{simple \: interest \: (S.I.)}}}$

${ \boxed{ \bold{ \blue{S.I. = \frac{P \times R\times T}{100}}}}}$

${ \bold{</strong><strong>S</strong><strong>.</strong><strong>I</strong><strong>. = \frac{x \times 8 \times 2}{100} }}$

${ \bold{ \implies{</strong><strong>S</strong><strong>.</strong><strong>I</strong><strong>.</strong><strong>= </strong><strong>Rs</strong><strong>. \frac{16x}{100}}}}$

${ \bold{ \underline{compound \: interest \: (</strong><strong>C.</strong><strong>I</strong><strong>.</strong><strong>)}}}$

${ \boxed { \bold { \blue{</strong><strong>C.</strong><strong>I</strong><strong>.</strong><strong> = </strong><strong>P</strong><strong>( {(1 + \frac{</strong><strong>R</strong><strong>}{100} )}^{</strong><strong>T</strong><strong>} - 1)}}}}$

C.I. = x(( 1 + 8/100)^2 -1)

=> C.I. = x (( 1+ 2/25)^2 - 1 )

=> C.I. = x ((27/25)^2 - 1 )

=> C.I. = x ( 729/625 - 1 )

=> C.I. = x (729-625)/625

=>. C.I. = Rs. 104x/625

according to the question......

C.I. - S.I. = Rs. 64

104x/625 - 16x/100 = Rs. 64

=> 104x/625 - 4x/25 = Rs. 64

=> (104x - (4x × 25))/625 = Rs. 64

=> (104x - 100x)/625 = Rs. 64

=> 4x/625 = Rs. 64

=> x = Rs. (64×625)/4

=> x = Rs. 16× 625

=> x = Rs. 10,000

therefore,

principal = Rs. 10,000