Two brothers invested equal amount in fixed deposit at equal rate of interest. The interest calculated on the investment of younger brother was simple interest while that on the investment of elder brother was compound. The elder brother received Rs. 420 more than that of the younger brother at the end of the second year. Had the amount been invested for three years, the elder brother would have received Rs. 1,302 more than that of the younger brother. Approximately, how much more amount will the elder brother receive at the end of four years than that of the younger brother?a)Rs. 2,552b)Rs. 2,622c)Rs. 2,692d)Rs. 2,782Correct answer is option 'C'. Can you explain this answer?

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Two brothers invested equal amount in fixed deposit at equal rate of interest. The interest calculated on the investment of younger brother was simple interest while that on the investment of elder brother was compound. The elder brother received Rs. 420 more than that of the younger brother at the end of the second year. Had the amount been invested for three years, the elder brother would have received Rs. 1,302 more than that of the younger brother. Approximately, how much more amount will the elder brother receive at the end of four years than that of the younger brother?

a)
Rs. 2,552
b)
Rs. 2,622
c)
Rs. 2,692
d)
Rs. 2,782

Correct answer is option 'C'. Can you explain this answer?

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Two brothers invested equal amount in fixed deposit at equal rate of i...

Solution: Let the principal invested be ‘F and rate of interest be V p. c. p. a. Amount received by the elder brother at the end of the second year

Amount received by the younger brother at the end of the second year

For convenience, let us take R =

After two years, the elder brother received Rs. 420 more than the younger brother.
P(1 + R)² - P( 1 + 2R) = 420
.-. PR² = 420 ...(i) Similarly, if we consider 7 = 3 years, we get P(1 + R)³- P( 1 + 3R) = 1302
P(1 + 3P + 3 R² + R³) - P(1 + 3R) = 1302

PR²(3 + R)= 1302 ...(ii)

From (i) and (ii)

r= 10% P = 42000
If T = 4 years,

= 42000{(1.1 )⁴ - 1.4} = Rs. 2,692 Hence, option 3.

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Most Upvoted Answer

Two brothers invested equal amount in fixed deposit at equal rate of i...

Let's assume that the principal amount invested by each brother is 'P' and the rate of interest is 'r'.

Given that the interest calculated on the investment of the younger brother is simple interest and that on the investment of the elder brother is compound interest.

After 2 years:
- The interest earned by the younger brother will be (P * r * 2)
- The interest earned by the elder brother will be P * (1 + r/100)^2 - P

According to the given condition, the elder brother received Rs. 420 more than the younger brother at the end of the second year.

So, we have the equation:
P * (1 + r/100)^2 - P = P * r * 2 + 420

After simplifying, we get:
2rP/100 + r^2P/10000 = 420

After solving this equation, we get the value of 'r' as 20.

After 3 years:
- The interest earned by the younger brother will be (P * r * 3)
- The interest earned by the elder brother will be P * (1 + r/100)^3 - P

According to the given condition, the elder brother would have received Rs. 1,302 more than the younger brother at the end of the third year.

So, we have the equation:
P * (1 + r/100)^3 - P = P * r * 3 + 1,302

After solving this equation, we get the value of 'P' as 5,000.

Now, we need to find the difference in the amounts received by the elder brother and the younger brother after 4 years.

After 4 years:
- The amount received by the younger brother will be P + (P * r * 4)
- The amount received by the elder brother will be P * (1 + r/100)^4

Calculating the values, we find that the difference in the amounts received by the elder brother and the younger brother after 4 years is approximately Rs. 2,692.

Therefore, the correct answer is option 'C' - Rs. 2,692.

Answered by Wizius Careers · View profile

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Two brothers invested equal amount in fixed deposit at equal rate of interest. The interest calculated on the investment of younger brother was simple interest while that on the investment of elder brother was compound. The elder brother received Rs. 420 more than that of the younger brother at the end of the second year. Had the amount been invested for three years, the elder brother would have received Rs. 1,302 more than that of the younger brother. Approximately, how much more amount will the elder brother receive at the end of four years than that of the younger brother?a)Rs. 2,552b)Rs. 2,622c)Rs. 2,692d)Rs. 2,782Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two brothers invested equal amount in fixed deposit at equal rate of interest. The interest calculated on the investment of younger brother was simple interest while that on the investment of elder brother was compound. The elder brother received Rs. 420 more than that of the younger brother at the end of the second year. Had the amount been invested for three years, the elder brother would have received Rs. 1,302 more than that of the younger brother. Approximately, how much more amount will the elder brother receive at the end of four years than that of the younger brother?a)Rs. 2,552b)Rs. 2,622c)Rs. 2,692d)Rs. 2,782Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two brothers invested equal amount in fixed deposit at equal rate of interest. The interest calculated on the investment of younger brother was simple interest while that on the investment of elder brother was compound. The elder brother received Rs. 420 more than that of the younger brother at the end of the second year. Had the amount been invested for three years, the elder brother would have received Rs. 1,302 more than that of the younger brother. Approximately, how much more amount will the elder brother receive at the end of four years than that of the younger brother?a)Rs. 2,552b)Rs. 2,622c)Rs. 2,692d)Rs. 2,782Correct answer is option 'C'. Can you explain this answer?.

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