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Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is

Correct answer is '20'. Can you explain this answer?
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Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and...
Solution:

Let Mr. Pinto's capital be Rs. 100.

Interest on 1/5 of his capital invested at 6% per annum for 1 year = (1/5) × 6 = 6/5

Interest on 1/3 of his capital invested at 10% per annum for 1 year = (1/3) × 10 = 10/3

Interest on the remaining amount invested at 1% per annum for 1 year = (3/15) × 1 = 1/5

Total interest earned in 1 year = (6/5) + (10/3) + (1/5) = 37/15

Let the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital be n.

Total interest earned in n years = (37/15) × n

According to the question, (37/15) × n ≥ 100

n ≥ (100 × 15)/37

n ≥ 40/37

n ≥ 2.70 (approx)

Therefore, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is 3.

But the correct answer is 1. Where is the mistake?

Mistake:

The question asks for the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital. It does not ask for the minimum number of years required for the total value of the investments to equal or exceed his initial capital.

Therefore, the correct approach is to find the total interest earned in 1 year and compare it with the initial capital. If the total interest earned is more than or equal to the initial capital, then the answer is 1, otherwise, it is more than 1.

Total interest earned in 1 year = (6/5) + (10/3) + (1/5) = 37/15

Since 37/15 is more than 100/1, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is 1.
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Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and...
My answer is 20, edurev's answer is 1 , guys please make sure me the right answer.
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A wealthy investor who wants to invest his money is approached by five counsellors who want to convince him to invest his money with their respective firms. Having very little knowledge of finance, the investor decides to just invest a certain sum of money with each one of them and judge for himself. He withdraws a total sum of 100000 from his bank account and gives different amounts of money to the five counsellors and gets a total profit of 22950 in return. After six months he makes the following observations about his money invested and the profits earned:1. The highest investment has given him the third lowest profit percentage.2. The least investment is two thousand less than half the highest investment.3. The second highest investment is twice the second lowest investment.4. The profit on the highest investment is 1/5 times the investment and the profit on the least investment is 50%.5. Three sums of his investments are in AP with 1000 as the common difference and all his investments are more than 10000.6. The profit percentage of the second lowest investment and the percentage share of the highest investment in total investment are the same.7. The least profit percent is 9% and the second lowest profit percentage is 2.5 percentage points less than the third lowest profit percentage.8. The second highest profit percent is 30%. Q. Which of the following investments has the largest percentage point difference between the profit percentage and the investment share?

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Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital isCorrect answer is '20'. Can you explain this answer?
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