Question

If the difference between the compound interest and simple interest on a certain sum of money for 2 years at 12 1/2℅ per annum is ₹150 . The sum is?
I know the answer that is 9600.
pls can anyone tell how to do it.
pls do it's urgent
if it's right I will mark brainliest.​

Answer 1

Let the amount be x,

then

simple interest for 1.5 years = 100PRT= 100x×12×1.5 =100

18x --(1)

compound interest for 1 year

CI=x(1+r)=x(1+0.12)=1.12x

for neat 6 months

CI= 1.12x(1+0.06)=1.872x

net compound interest

CI=1.872x-x=0.1872x

now given CI-SI=150

0.1872x - 0.18x =150

0.0072x=150

x=

0.0072

150

=20,833.33 RS.

∴ The total amount is 20,833.33 RS.

Answer 2

♠ Solution :-

♣ Provided :-

• Time → 2 years
• Rate of Interest → 12½ % ⇒ 25/2 %
• Difference between C.I and S.I is ₹150

♣ Assumption :-

• Let the Principal be p

♣ Let's Start !

Simple Interest :-

we know that :-

$\large\boxed{\mathtt\blue{S.I=\frac{P×R×T}{100}}}$

where,

♦ P = principal

♦ R = Rate

♦ T = Time

$\large{\mathtt{⟹S.I=\frac{p×25×2}{2×100}}}$

♦ Which simplifies to :-

$\large{\mathtt{∴S.I=\frac{p}{4}}}$

Compound Interest :-

we know that :-

$\large\boxed{\mathtt\blue{C.I=P(1+\frac{r}{100})ⁿ-p}}$

where,

• r = rate

• n = time

• p = principal

$\large{\mathtt{⟹C.I=p(1+\frac{25}{100×2})²-p}}$

Which simplifies to :-

$\large{\mathtt{∴C.I=\frac{17p}{64}}}$

♣ Finalization :-

Given in Question that:-

⇒ C.I - S.I = 150

⇒ $\large{\mathtt{\frac{17p}{64}-\frac{p}{4}=150}}$

⇒$\large{\mathtt{\frac{p}{64}=150}}$

⇒$\large{\mathtt{∴p=9600}}$

♣ Answer :-

The principal amount or the sum of money is ₹ 9,600.