Question

divide rupees 195150 between a and b that amount a receives in 2 years is same as that b receives in 4 years. the interest is compounded annually at the rate of 4 percent​

Answer 1

Given:–

• Amount received by a in 2 years is same as amount received by b in 4 years.
• Rate of interest compounded annually = 4%

To find:–

• We have to divide Rs.195150 between a and b.

Formulas used:–

• $\boxed{\text{A} = \text{P}(1 + \dfrac{\text{r}}{100} ) {}^{n} }$

where,

• A = Amount

• P = Principal

• r = Rate of interest

• n = Time taken

Assumptions:–

• Let amount received by a be y

Some common terms:–

• The money borrowed is called the Principal, the extra money paid for using lender's money is called the interest and the total money, paid to the lender at the end of the specified period is called the amount.

Step by step explaination:-

☯ As we know amount received by a is Rs.y. Therefore, amount received by b would be (195150-y)

☯ Calculating the value of y. That is by evaluating values in the given formula of amount.

$\implies \: \text{y}(1 + \dfrac{4}{100} ) {}^{2} = (195150 - \text{y})(1 + \dfrac{4}{100}) {}^{4}$

$\implies \: \text{y} \: \cancel{(1 + \dfrac{4}{100}){}^{2}} = (195150 - \text{y})\cancel{(1 +\dfrac{4}{100}) {}^{2} }$

$\implies \: \text{y} = (195150 - \text{y})(1 + \dfrac{4}{100} ) {}^{2}$

$\implies \: \text{y} = (195150 - \text{y})(1 + \dfrac{4}{100} )(1 + \dfrac{4}{100})$

$\implies \: \text{y} = (195150 - \text{y})(1.04) {}^{2}$

Opening brackets

$\implies \text{y} =(195150 \times 1.0816) - \text{1.0816y}= 211074.24 - 1.0816y$

Bringing the R.H.S. into L.H.S.

$\implies\: \text{1.0816y + y} = 211074.24$

$\implies\: \text{2.0816y} = 211074.24$

Cancelling both the sides (i.e. dividing)

$\implies\: \text{y} = \dfrac {\cancel{211074.24}} {\cancel{2.0816}}$

$\implies \: \text{y} = 1,01,400$

Conclusion:–

At last, calculating the amount received by a and b.

$\implies\: \text{a} = \text{Rs 101400}$$\implies \: \text{b} = \text{(195150-y)}\rightarrow (195150-101400) \rightarrow \text{Rs.93750}$

Therefore,

a = Rs.101400

b = Rs.93750

Answer 2

Given :

• Amount received by a in 2 years is same as amount received by b in 4 years.
• Rate of interest compounded annually = 4%

To find :

• We have to divide Rs. 195150 between a and b

Formula used :

$\: \: \: \: \: \: \: \: \: \: \: \: \rm\boxed{ \underline{\text{A} = \text{P}(1 + \dfrac{\text{r}}{100} ) {}^{ \rm \: n} }}$

And We know that,

• A = Amount

• P = Principal

• r = Rate of interest

• n = Time taken

Solution :

$\: \: \purple❍ \: \underline{\boxed{ \rm \text{y}(1 + \dfrac{4}{100} ) {}^{2} = (195150 - \text{y})(1 + \dfrac{4}{100}) {}^{4}}}$

$\: \: \: \: \: \: \: \: \: \: \: \boxed{ \underline{ \rm\text{y} \: \cancel{(1 + \dfrac{4}{100}){}^{2}} = (195150 - \text{y})\cancel{(1 +\dfrac{4}{100}) {}^{2}}}}$

$\: \: \ \: \boxed{ \rm\text{y} = (195150 - \text{y})(1 + \dfrac{4}{100}){}^{2}}$

$\: \: \boxed{ \rm\text{y} = (195150 - \text{y})(1 + \dfrac{4}{100} )(1 + \dfrac{4}{100})}$

$\: \: \: \: \: \: \boxed{\boxed{ \red{\rm\text{y} = (195150 - \text{y})(1.04) {}^{2}}}}$

Open the brackets :-

$\: \: \: \: \: \: \: \boxed{\underline{\rm\text{y} =(195150 \times 1.0816) - \text{1.0816y}= 211074.24 - 1.0816y}}$

R.H.S. into L.H.S.

$\: \: \: \boxed{\rm{1.0816y + y} = 211074.24}$

$\: \: \: \: \implies\rm{2.0816y} = 211074.24$

★ Cancelling both the sides

$\implies\rm{y} = \dfrac {\cancel{211074.24}} {\cancel{2.0816}}$

$\: \: \: \: : \: \longmapsto \rm{y} = 1,01,400$

★ At last :-

calculating the amount received by a and b.

$\rm⟹a=Rs 101400 \\ \\ \rm{b} = \rm{(195150-y)} \\ \\ \rightarrow(195150-101400) \\ \\ \rightarrow \rm{Rs.93750}$

★ Therefore the final answer is :

A = Rs. 101400

B = Rs. 93750

◆ Hence, verified.