Question

23 The difference between C.I. and S.I. on a certain principal at 8% p.a. for two years is `16. Find the sum of money

Answer 1

${\huge{\underline {\mathfrak {\green {Question}}}}}$

The difference between C.I. and S.I. on a certain principal at 8% p.a. for two years is `16. Find the sum of money.

_________________________

${\huge{\underline {\mathfrak {\green {Answer}}}}}$

${\boxed{\tt{\red {Given:}}}}$

Rate = 8%

Time = 2 years

Difference between S.I & C.I = 16

_____________________________________

${\boxed{\tt{\red {Find:}}}}$

The sum of money = ?

_____________________________________

${\boxed{\tt{\red {Solution:}}}}$

Let the sum = P

SI = $\frac {PRT}{100}$

SI = $\frac {P×8×2}{100}$

SI = $\frac {16P}{100}$

For Finding CI ,

=$A = P ({1 + \frac{R}{100}})^{n}$

=$A = P({1 + \frac {8}{100}})^{2}$

= $A = P ({ \frac{108}{100}})^{2}$

=$A = P ({\frac {54}{50}})^{2}$

=$A = \frac {2916P}{2500}$

C.I = A - P

=$\frac {2916P}{2500}-P$

=$\frac{2916P-2500P}{2500}$

=$\frac{416P}{2500}$

ATQ,

= CI - SI = 16

= $</strong>\frac<strong> {</strong><strong>4</strong><strong>16P}{2500}-</strong><strong>\frac{</strong><strong>16</strong><strong>P}</strong><strong>{</strong><strong>1</strong><strong>00}</strong><strong>$ = 16

$= \frac {16P}{2500}$= 16

= P = 2500

_________________________