Question

Pooja borrowed a certain sum for two years at simple interest from Mona. Pooja lent this sum to Sonia at same rate for two years compounded annually. At the end of two years Pooja received ₹205 as compound interest but paid ₹200 as simple interest. Find the sum and rate of interest.​

Answer 1

Answer:

S.I= 5% and C.I= ₹2,000

Step-by-step explanation:

Answer 2

Answer:

The rate of interest = 5%

The certain sum  = ₹ 2000

Step-by-step explanation:

Given data

Pooja borrowed a certain sum for two years at simple interest from Mona

and lent this same amount at same rate of interest to Sonia

the compound interest received by Pooja end of 2 years = ₹ 205

the simple interest paid to Sonia = ₹ 200  

here we need to find certain sum

Let P be the sum, R be the rate of interest and time period is 2 years.

simple interest on P, I = $\frac{PTR}{100}$  which is equals to ₹ 200

                                   $\frac{P(2)R}{100} = 200$

                                      PR = 200(100)/ 2

                                      P = 10000 / R _(1)

compound interest on P, C.I = $P[1 + \frac{R}{100} ]^{T} - P$  which is equals to 205

                                  ⇒      $\frac{10000}{P} [ 1+\frac{R}{100} ]^{2} - \frac{10000}{R} = 205$

                                  ⇒     $\frac{10000}{R} [(\frac{100+R}{100})^{2} - 1] = 205$

                                 ⇒      $\frac{(100+R)^{2} }{100^{2} } - 1 = \frac{205R}{10000}$

                                  ⇒   $\frac{(100+R)^{2} - 10000 }{10000} = \frac{205R}{10000}$

                                  ⇒   $10000 +R^{2}+200R - 10000 = 205R$  

                                  ⇒    R² + 200 R  = 205 R

                                  ⇒    R (R+200) = 205 R

                                  ⇒    R + 200 = 205

                                  ⇒    R = 5

⇒ the rate of interest R = 5%  

⇒ the sum P = 10000/R = 10000/ 5 = ₹ 2000