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Mathematics

Assertion (A): On a certain sum, the C.I for consecutive three years at 5% rate is ₹ 420, ₹ 441 and ₹ 460.05, the sum is ₹ 420.

Reason (R): The sum is ₹ 420 - 5% of ₹ 420.

  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

Both A and R are false.

Explanation

Given,

C.I. for first year = ₹ 420

R = 5 %

T = 3 years

For 1st year,

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

⇒ 420 = P×5×1100\dfrac{P \times 5 \times 1}{100}

⇒ P = 42,0005\dfrac{42,000}{5}

⇒ P = ₹ 8,400

∴ The sum is ₹ 8,400, not equal ₹ 420.

∴ Assertion (A) is false.

Given,

Sum = ₹ 420 - 5% of ₹ 420

= ₹ 420 - 5100×\dfrac{5}{100} \times ₹ 420

= ₹ 420 - 120×\dfrac{1}{20} \times ₹ 420

= ₹ 420 - 21

= ₹ 399

∴ The sum is ₹ 8,400, not equal to ₹ 420.

∴ Reason (R) is false.

Hence, Both Assertion (A) and Reason (R) are false.

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