Question

.Sahil’s capital is 1/6 times more than Chaya’s capital. Chaya invested her capital at 20 % per annum for 2 years (compounded annually). At what rate % p.a. simple interest should Sahil invest his capital so that after 2 years, they both have the same amount of capital?​

Answer 1

Answer:

115/7%

Step-by-step explanation:

Let, the capital of Sahil = 6. ∴ Capital of Chaya = 7

Simple Interest & Compound Solved = 11 5/7%

Answer 2

Rate % per annum simple interest should Sahil invest his capital  is  11.91%.

Step-by-step explanation:

Given:

Capital of Sahil’s  is 1/6 times more than Chaya’s capital.

Invested capital  by Chaya  at 20 % per annum for 2 years (compounded annually).

Sahil invested his capital so that after 2 years on simple interest.

Both they have the same amount of capital.

To Find:

Rate % per annum simple interest should Sahil invest his capital  is

Formula Used:

$SI=\frac{MSR}{100}$             -------------------------------------- formula no 01.

Where SI = simple interest

M = principal

R = interest rate (in percentage)

S= time duration (in years)

Amount (A) = Principal (M) + Interest (R)

$X= Y(1+\frac{Z}{100} )^{T}$                           ---------------------------------------formula no.02

X= represents the new principal sum or the total amount of money after compounding period

Y= represents the original amount or initial amount

Z= is the annual interest rate(in percentage)

T= represents the number of years

Solution:

As given- Capital of Sahil’s  is 1/6 times more than Chaya’s capital.

Let the capital of Chaya Y is K.  

Then Sahil’s capital $M=K+\frac{K}{6}$

                                  $M=\frac{7K}{6}$   ------- equation no.01

As given- Invested capital  by Chaya  at 20 % per annum for 2 years (compounded annually).

             T= 2 years , Z= 20 %

Applying formula no.01.  

$X= Y(1+\frac{Z}{100} )^{T}$

$X= K(1+\frac{20}{100} )^{2}$

$X= K\frac{120}{100}$

$X=1.44K$    

Total  amount of Chaya  $X=1.44K$  ------------------------- equation no.02

As given - Sahil invested his capital so that after 2 years on simple interest.

Applying formula no.02.

S=2 Years   ,     $M=\frac{7K}{6}$ ( from equation 01)

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

$SI=\frac{(\frac{7K}{6} )\times 2 \times R}{100}$

$SI=\frac{14KR}{600}$

$SI=0.023 KR$     ----------------  equation no.03

Total  amount of Sahil  $A=M+SI$

                                     $A= \frac{7K}{6} +0.023KR$

                                       $A=1.166K+0.023 KR$  

As given - Both they have the same amount of capital.

Total  amount of  Chaya = Total amount of Sahil

Putting the values of X and A  form equation 2 and equation 3 , we get.

$1.44K=1.166K+0.023 KR$

$0.274K=0.023 KR$

$R=\frac{0.274}{0.023}\%$

$R= 11.91 \%$

Thus, the Rate % per annum simple interest should Sahil invest his capital  is  11.91%.