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Mathematics

Assertion (A): A certain sum is lent for four years at 10% per annum, the amount for the second year is ₹ 1.21 x the sum lent.

Reason (R): C.I. for second year is equal to 1.21 times the sum lent.

  1. A is true, R is false.
  2. A is false, R is true.
  3. Both A and R are true.
  4. Both A and R are false.

Compound Interest

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Answer

A is true, R is false.

Explanation

Given,

R = 10%

T = 4 years

Let the sum be P.

Interest = P×R×T100\dfrac{P \times R \times T}{100}

Interest for first year = P×1×10100\dfrac{P \times 1 \times 10}{100} = P10\dfrac{P}{10}

Amount at end of first year = P + P10\dfrac{P}{10} = 11P10\dfrac{11P}{10}

Interest for second year = 11P10×10100\dfrac{11P}{10} \times \dfrac{10}{100} = 11P100\dfrac{11P}{100}

Amount at end of first year = 11P100\dfrac{11P}{100} + 11P = ₹ 121P100\dfrac{121P}{100} = ₹ 1.21 x P

∴ Assertion (A) is true.

Compound Interest for second year = 11P100\dfrac{11P}{100}

11P100\dfrac{11P}{100} ≠ 1.21P

∴ Reason (R) is false.

Hence, Assertion (A) is true and Reason (R) is false.

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