Assertion (A): A certain sum of ₹ 12,000 is lent at 10% per annum compound interest. The amount at the end of three years will be ₹ 12,000 + 20% of ₹ 12,000.

Reason (R): The amount at the end of five years = ₹ $12,000 \times \dfrac{11}{10} \times \dfrac{11}{10}$.

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.

Both A and R are false.

Explanation

Given,

P = ₹ 12,000, R = 10%, T = 3 years

Interest for first year : ₹ 12,000 x $\dfrac{10}{100}$ = ₹ 1,200

Amount at end of first year : ₹ 12,000 + ₹ 1,200 = ₹ 13,200

Interest for second year : ₹ 13,200 x $\dfrac{10}{100}$ = ₹ 1,320

Amount at end of second year : ₹ 13,200 + ₹ 1,320 = ₹ 14,520

Interest for third year : ₹ 14,520 x $\dfrac{10}{100}$ = ₹ 1,452

Amount at end of third year : ₹ 14,520 + ₹ 1,452 = ₹ 15,972

According to assertion,

amount = ₹ 12,000 + 20% of ₹ 12,000

= ₹ $12,000 + \dfrac{20}{100} \times 12,000$

= ₹ 12,000 + 2,400

= ₹ 14,400

Since the correct amount at the end of three years is ₹ 15,972 and not ₹ 14,400.

∴ Assertion(A) is false.

Given,

From the assertion,

Amount at end of third year = ₹ 15,972

Interest for fourth year : ₹ 15,972 x $\dfrac{10}{100}$ = ₹ 1,597.2

Amount at end of fifth year : ₹ 15,972 + ₹ 1,597.2 = ₹ 17,569.2

Interest for fifth year : ₹ 17,569.2 x $\dfrac{10}{100}$ = ₹ 1,756.92

Amount at end of fifth year : ₹ 17,569.2 + ₹ 1,756.92 = ₹ 19,326.12

According to reason,

The amount at the end of fifth year = ₹ $12,000 \times \dfrac{11}{10} \times \dfrac{11}{10}$

= $12,000 \times \dfrac{121}{100}$

= 14520

Since the correct amount at the end of five years is ₹ 19,326.12 and not ₹ 14,520.

∴ Reason(R) is false.

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