Question

Reena borrowed from Kamila certain sum for two years at simple interest Reena lent this to Hamid at the same rate for two years compound interest. At the end of two years she received Rs 110 as compound interest but paid Rs 100 as simple interest. Find the sum and rate of interest.​

Answer 1

Answer:

Sum = Rs. 250

Rate = 20%

Step-by-step explanation:

$\fcolorbox{purple}{pink}{Given:-}$

• Reena borrowed from Kamila certain sum for two years at simple interest Reena lent this to Hamid at the same rate for two years compound interest. At the end of two years she received Rs 110 as compound interest but paid Rs 100 as simple interest

$\fcolorbox{purple}{pink}{To \: Find:- }$

• Sum and rate of interest.

$\fcolorbox{purple}{pink}{Solution:- }$

As we know that

$\pink{ \boxed{ \bf \begin{array}{c} \ \bf CI = P \bigg \{ { \bigg(1 + \frac{R}{100} \bigg) }^{n} - 1 \bigg \} \\ \\ \rm \: And\\ \\ \bf SI = \frac{P \times R \times \: T} {100} \end{array}}}$

So,

$\rm \: SI = \frac{PRT}{100} \\ \dashrightarrow \rm \: 100 = \frac{PR \times 2}{100} \\ \dashrightarrow \rm \: PR = \frac{100 \times \cancel{100}}{ \cancel2} \\ \dashrightarrow \rm \fcolorbox{green}{blue}{PR = 5000}$

Also,

$\sf \: CI = P \bigg \{ { \bigg(1 + \frac{R}{100} \bigg) }^{n} - 1 \bigg \} \\ \longrightarrow \sf \: 110 = P \bigg \{ { \bigg(1 + \frac{R}{100} \bigg) }^{2} - 1 \bigg \} \\ \longrightarrow \sf \: 110 = P \bigg \{ \: \cancel1 + \frac{ \cancel2R}{ \cancel{100}} + \frac{ {R}^{2} }{10000} - \cancel1 \bigg \} \\ \longrightarrow \sf \: 110 = P \bigg \{ \: \frac{R}{50} + \frac{ {R}^{2} }{10000} \bigg \} \\ \longrightarrow \sf \: 110 = \frac{PR}{50} + \frac{PR}{10000} \times R \\ \longrightarrow \sf \: 110 = \frac{5000}{50} + \frac{5000}{10000} \times R \\ \sf \: \longrightarrow \: 110 = 100 + \frac{R}{2} \\ \longrightarrow \sf\: \frac{R}{2} = 110 - 100 \\ \longrightarrow \sf \: \frac{R}{2} = 10 \\ \longrightarrow \sf \: \fcolorbox{pink}{green}{R = 20\%}$

Now we get R as 20%

So,

PR = 5000

P = 5000/20

Sum = Rs. 250

Answer

Sum = Rs. 250

Rate% = 20%

Answer 2

Answer:

So,

PR = 5000

P = 5000/20

Sum = Rs. 250

Answer

Sum = Rs. 250

Rate% = 20%