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A certain sum amounts to rs 15748 in 3 years at simple interest at r % p. a. the same sum amounts to rs 16510 at (r 2) % p. a. Simple interest in the same time . What is the value of r? a) 10% b) 8% c) 12% d) 6%?
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A certain sum amounts to rs 15748 in 3 years at simple interest at r %...
Given:

Principal amount = P

Time = 3 years

Simple interest rate = r% p.a.

Amount after 3 years at r% p.a. = Rs. 15748

Amount after 3 years at (r+2)% p.a. = Rs. 16510

To find:

Simple interest for the same time period at (r+2)% p.a.

Value of r

Solution:

1. Calculation of Simple Interest

Simple Interest (SI) = P * R * T / 100

Where P is the principal, R is the rate of interest and T is the time period.

Let SI1 be the simple interest at r% p.a.

SI1 = P * r * 3 / 100

SI1 = 3Pr / 100

Let SI2 be the simple interest at (r+2)% p.a.

SI2 = P * (r+2) * 3 / 100

SI2 = 3P(r+2) / 100

SI2 - SI1 = 3P(r+2) / 100 - 3Pr / 100

SI2 - SI1 = 6P / 100

SI2 - SI1 = 0.06P

2. Calculation of Value of r

Amount after 3 years at r% p.a. = P + SI1

15748 = P + 3Pr / 100

15748 = P(1 + 3r / 100)

Amount after 3 years at (r+2)% p.a. = P + SI2

16510 = P + 3P(r+2) / 100

16510 = P(1 + 3(r+2) / 100)

Dividing equation 2 by equation 1, we get:

16510 / 15748 = (1 + 3(r+2) / 100) / (1 + 3r / 100)

1.048 = 1 + 0.03r / (1 + 3r / 100)

1.048(1 + 3r / 100) = 1 + 0.03r

1.048 + 0.03144r = 1 + 0.03r

0.01844r = 0.048

r = 0.048 / 0.01844

r = 2.6

Therefore, the value of r is 2.6%.

Answer: Option D (6%) is not among the given options. The closest option is Option B (8%).
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A certain sum amounts to rs 15748 in 3 years at simple interest at r % p. a. the same sum amounts to rs 16510 at (r 2) % p. a. Simple interest in the same time . What is the value of r? a) 10% b) 8% c) 12% d) 6%?
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A certain sum amounts to rs 15748 in 3 years at simple interest at r % p. a. the same sum amounts to rs 16510 at (r 2) % p. a. Simple interest in the same time . What is the value of r? a) 10% b) 8% c) 12% d) 6%? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A certain sum amounts to rs 15748 in 3 years at simple interest at r % p. a. the same sum amounts to rs 16510 at (r 2) % p. a. Simple interest in the same time . What is the value of r? a) 10% b) 8% c) 12% d) 6%? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain sum amounts to rs 15748 in 3 years at simple interest at r % p. a. the same sum amounts to rs 16510 at (r 2) % p. a. Simple interest in the same time . What is the value of r? a) 10% b) 8% c) 12% d) 6%?.
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