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Kamala borrowed from Ratan a certain sum at a certain rate for two years simple interest. She lent this sum at the same rate to arti for two years compound interest. At the end of two years, she received Rs. 210 as compound interest, but paid Rs. 200 only as simple interest. Find the sum and the rate of interest.

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Rs.1000, 10%

Rs.1200, 16%

Rs.1500, 1.6%

Rs.1830, 30%

answer is B.

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Detailed Solution

Given,
C.I. (Kamala received) = Rs 210
S.I. (Kamala paid) = Rs 200
Time period, t = 2 years
Let r be the interest rate and P be the principal amount
Apply the compound interest formula,

C I = P 1 + r 100 t − P

Now substitute t = 2, CI = 210

⇒ 210 = P 1 + r 100 2 − P ⇒ 210 = P 1 + r 2 10000 + 2 r 100 − P ⇒ 210 = r 2 P 100000 + 2 r P 100 ...... (1)

Apply the simple interest formula,

S I = P r 100 t

Now substitute t = 2, SI = 200

⇒ 200 = P r 100 2 ⇒ P r = 10000 … … (2)

Substitute the value of P and r from equation (2) in equation (1)

⇒ 210 = 10000 r 10000 + 20000100 ⇒ 210 = r + 200 ⇒ r = 210 − 200 ⇒ r = 10 %

Substitute the value of r in equation (2)

⇒ P 10 = 10000 ⇒ P = Rs 1000

Thus, the required sum is Rs 1000 and the required interest rate is 10% per annum.
Hence, the correct option is 2.

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