# Find the Sum.

The compound interest on a certain sum for 2 year is Rs 105 and simple interest is Rs 100. Find the sum.

- Rs. 300
- Rs. 500
- Rs. 400
- Rs. 600

**Answer: (2) Rs.500**

**Explanation:-**

Let the principal be Rs.X

**Given-**

Time = 2 years, Compound Interest = Rs.105 & Simple Interest = Rs.100

**Formula-**

**The ratio of Compound Interest & Simple Interest same sum at R % for N years .**

**Then, C I /S I = R /N x 100 + 1**

Then, 105 / 100 = R / 2 x 100 + 1

21 / 20 = R/ 200 + 1

21 / 20 = (R + 200) / 200

21 x 200 = (R + 200) x 20

4200 = 20 R + 4000

20 R = 4200 – 4000

20 R = 200

R = 200/20

R = 10 %

**Formula-**

**Simple Interest = P x R x T/100**

**Where, P = principal , R = rate, & T = time.**

Then, 100 = X x 10 x 2 /100

100 = 20 X /100

20 X = 100 x 100

20 X = 10000

X = 10000/20

X = 1000/2

X = Rs.500

Then, the sum is Rs.500

Hence, the answer is (2) Rs.500.