Question

Aman divided 90756 between Pooja and Prem and they invest their money at 5% and 8% per annum compound interest respectively such that they both receive equal amount at the end of 2 years. find the share of each​.

Answer 1

$\sf \orange{\underline{Given : }}$

• Aman divided an amount of sum of ₹90,756 among Pooja and Prem.

• They (Pooja and Prem) invested their sum in 5% and 8% p.a.(per annum) for 2 year.

$\sf \orange{\underline{To \: find : }}$

• The share that was shared between them

2 years ago.

$\sf \orange{\underline{Solution : }}$

We know that,

${ \underline{ \boxed{ \blue{ \sf A(amount) = P(1+\frac{r}{100}{)}{2}}}}}$

So, let's assume that the Pooja's share is ₹x.

Then, Prem's share will be ₹(90,756 - x)

Where,

➠ $\bf \green{\underline{Calculation \: of \: Pooja : }}$

P(principal) = ₹x.

R(rate) = 5%.

n(time) = 2 years.

${ \red{ \longmapsto {\pink{ \sf \: x {(1 + \frac{r}{100}) }^{2} }}}}$

➠$\bf \green{\underline{ Calculation \: for \: Prem : }}$

P(principal) = ₹(90,756 - x).

R(rate) = 8%.

n(time) = 2 years.

${ \red{ \longmapsto {\pink{ \sf (90756 - x) {(1 + \frac{r}{100}) }^{2} }}}}$

NOW,

As it is told that they gets same amount after a duration of 2 years.

Hence,

We can write it as :

$\implies\bf \: x {(1 + \frac{r}{100}) }^{2}= \bf (90756 - x) {(1 + \frac{r}{100}) }^{2}$

☯ According to the question,

Substituting the given values :

$\implies\bf \: x {(1 + \frac{5}{100}) }^{2}= \bf (90,756 - x) {(1 + \frac{8}{100}) }^{2}$

$\bf \implies \: x {( \frac{105}{100} )}^{2} = (90,756 - x) ({\frac{108}{100}}^{2})$

$\bf \implies \: \frac{ x({105})^{2} }{ {100}^{2} } = \frac{ (90,756 - x) {(108)}^{2} }{ {100}^{2} }$

${ \bf \implies \: \frac{ x({105})^{2} }{ { \cancel{100}}^{2} } = \frac{ (90,756 - x) {(108)}^{2} }{ { \cancel{100}}^{2} } }$

$\bf \implies x({105})^{2} = (90,756 \times {108}^{2} ) - x({108})^{2}$

$\bf \implies 11,025 {x} = (90,756 \times {108}^{2} ) - 11,664x$

$\bf \implies 11,025 {x} + 11,664 {x} = (90,756 \times 11,664 )$

$\bf \implies 22,689 {x} = (90,756 \times 11,664 )$

$\bf \implies \: x = \frac{(90,756 \times \cancel{11,664 })}{\cancel{22,689}}$

$\bf \implies x = \frac{\cancel{90,756} \times {1,296}}{\cancel{2,521}}$

$\bold \gray \dag { \underline{ \boxed{ \blue{ \bf \therefore \: x = 46,656}}}}\bold \gray \dag$

Hence,

After solving the equation we get :

➠ x = ₹46,656 ➝ Pooja's share

Therefore,

Prem's share will be :

➠ ₹(90,756 - x)

➠ ₹(90,756 - 46,656)

➠ ₹ 44,100 ➝ Prem's share

THUS,

${ \underline{ \boxed{ \blue{ \bf{ ☯ Required \: answer : }}}}}$

${ \underline{ \boxed{ \orange{ \red \odot\mid \bf{Pooja's \: share \to \: 46,565 {\checkmark}}}}}}$

${ \underline{ \boxed{ \green{ \red \odot\mid \bf \: Prem's \: share \to 44,100 {\checkmark}}}}}$

Answer 2

Step-by-step explanation:

wah bhai kaise kr lete ho Aaisa ans