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Select the correct answerThe ratio of expenditure and savings of a person is 5 : 3. If the income increases by 20% and the expenditure increases by 10%, then the person’s savings increase by?Options36 2/3%13 1/3%30 1/3%3 1/3%

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Select the correct answerThe ratio of expenditure and savings of a person is 5 : 3. If the income increases by 20% and the expenditure increases by 10%, then the person’s savings increase by?Options36 2/3%13 1/3%30 1/3%3 1/3%

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Solution 1

Let's solve this step by step:

  1. Let's assume the person's income is xx. According to the problem, the ratio of expenditure to savings is 5:3. This means that if the person's income is divided into 8 parts, 5 parts are spent and 3 parts are saved.

  2. So, the expenditure = 5x/8 and the savings = 3x/8.

  3. The problem states that the income increases by 20%. So, the new income = x + 20% of x = 1.2x.

  4. It also states that the expenditure increases by 10%. So, the new expenditure = 5x/8 + 10% of 5x/8 = 1.1 * 5x/8.

  5. The new savings can be found by subtracting the new expenditure from the new income. So, new savings = 1.2x - 1.1 * 5x/8.

  6. To find the percentage increase in savings, we subtract the original savings from the new savings, divide by the original savings, and then multiply by 100.

Doing the math, we find that the percentage increase in savings is approximately 36 2/3%. So, the correct answer is 36 2/3%.

This problem has been solved

Solution 2

Let's solve this step by step:

  1. Let's assume the person's income is xx. According to the problem, the ratio of expenditure to savings is 5:3. This means that out of every 8 parts of his income, 5 parts are spent and 3 parts are saved. So, his expenditure is 5x/8 and his savings are 3x/8.

  2. The problem states that the income increases by 20%. So, the new income is 1.2x.

  3. The expenditure increases by 10%. So, the new expenditure is 1.1 * (5x/8) = 5.5x/8.

  4. The new savings can be found by subtracting the new expenditure from the new income. So, the new savings are 1.2x - 5.5x/8 = 9.6x/8 - 5.5x/8 = 4.1x/8 = 0.5125x.

  5. To find the percentage increase in savings, we subtract the original savings from the new savings, divide by the original savings, and multiply by 100. So, the percentage increase in savings is ((0.5125x - 3x/8) / (3x/8)) * 100 = (0.5125 - 0.375) / 0.375 * 100 = 36.67%.

So, the correct answer is 36 2/3%.

This problem has been solved

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