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Mathematics

Statement 1: If P is the sum invested for 2 years at 20% rate of interest

= ₹ P x 20100×20100\dfrac{20}{100} \times \dfrac{20}{100}

Statement 2: Interest accrued in 2 years = ₹ (P x 120100×120100−P)\dfrac{120}{100} \times \dfrac{120}{100} - P)

  1. Both the statements are true.

  2. Both the statements are false.

  3. Statement 1 is true, and statement 2 is false.

  4. Statement 1 is false, and statement 2 is true.

Compound Interest

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Answer

Let ₹ P be the principal amount, R be the rate of interest and n be time.

A=P(1+R100)n=P(1+20100)2=P(120100)2=P×120100×120100.A = P\Big(1 + \dfrac{R}{100}\Big)^n \\[1em] = P\Big(1 + \dfrac{20}{100})^2 \\[1em] = P\Big(\dfrac{120}{100}\Big)^2 \\[1em] = P \times \dfrac{120}{100} \times \dfrac{120}{100}.

Thus, Statement 1 is false.

C.I. = A - P

= P×120100×120100−PP \times \dfrac{120}{100} \times \dfrac{120}{100} - P

Thus, Statement 2 is true.

Hence, option 4 is correct option.

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