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Karishma expenditure and savings are in the ratio 5 : 3. Her income increases by 15%. Her expenditure also increases by 18%. By how many % does he saving increase?
- a)13%
- b)10%
- c)7%
- d)20%
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Karishma expenditure and savings are in the ratio 5 : 3. Her income in...
GIVEN:
Ratio of Expenditure and Savings = 5:3
FORMULA USED:
Percentage Increase in saving = [(New savings - old savings)/old savings] × 100
CALCULATION:
Let expense = 500, savings = 300 & income = 800
So new expense = 500 + 18% of 500 = 500 + 90 = 590 & new income = 800 + 15% of 800 = 800 + 120 = 920
So new savings = 920 - 590 = 330
∴ Required percentage increase in savings = (330 - 300)/300 × 100 = 30/300 × 100% = 10%
Most Upvoted Answer
Karishma expenditure and savings are in the ratio 5 : 3. Her income in...
Let's assume that Karishma's initial expenditure is 5x and her initial savings are 3x, where x is some constant.
Increase in Income:
Karishma's income increases by 15%, which means her new income is 115% of her initial income. Therefore, her new income is 1.15 times her initial income.
Increase in Expenditure:
Karishma's expenditure increases by 18%, which means her new expenditure is 118% of her initial expenditure. Therefore, her new expenditure is 1.18 times her initial expenditure.
Calculating the new expenditure and savings:
Since her initial expenditure is 5x, her new expenditure is 1.18 * 5x = 5.9x.
Similarly, her initial savings are 3x, and her new savings can be calculated by subtracting the new expenditure from the new income.
New savings = (1.15 * initial income) - (1.18 * initial expenditure)
= 1.15 * (3x/5) - 1.18 * 5x
= 3.45x/5 - 5.9x
= (3.45x - 5.9x)/5
= -2.45x/5
= -0.49x
Calculating the percentage increase in savings:
The percentage increase in savings can be calculated by dividing the increase in savings by the initial savings and multiplying by 100.
Percentage increase in savings = (new savings - initial savings) / initial savings * 100
= (-0.49x - 3x) / 3x * 100
= (-3.49x) / 3x * 100
= -349/3 %
Since the percentage increase in savings is negative, it means that Karishma's savings have decreased. However, the question asks for the percentage increase, so we take the absolute value of the percentage decrease.
Percentage increase in savings = 349/3 %
≈ 116.33 %
Therefore, the percentage increase in savings is approximately 116.33%. None of the given options match this answer, so there seems to be an error in the question or the options provided.
Increase in Income:
Karishma's income increases by 15%, which means her new income is 115% of her initial income. Therefore, her new income is 1.15 times her initial income.
Increase in Expenditure:
Karishma's expenditure increases by 18%, which means her new expenditure is 118% of her initial expenditure. Therefore, her new expenditure is 1.18 times her initial expenditure.
Calculating the new expenditure and savings:
Since her initial expenditure is 5x, her new expenditure is 1.18 * 5x = 5.9x.
Similarly, her initial savings are 3x, and her new savings can be calculated by subtracting the new expenditure from the new income.
New savings = (1.15 * initial income) - (1.18 * initial expenditure)
= 1.15 * (3x/5) - 1.18 * 5x
= 3.45x/5 - 5.9x
= (3.45x - 5.9x)/5
= -2.45x/5
= -0.49x
Calculating the percentage increase in savings:
The percentage increase in savings can be calculated by dividing the increase in savings by the initial savings and multiplying by 100.
Percentage increase in savings = (new savings - initial savings) / initial savings * 100
= (-0.49x - 3x) / 3x * 100
= (-3.49x) / 3x * 100
= -349/3 %
Since the percentage increase in savings is negative, it means that Karishma's savings have decreased. However, the question asks for the percentage increase, so we take the absolute value of the percentage decrease.
Percentage increase in savings = 349/3 %
≈ 116.33 %
Therefore, the percentage increase in savings is approximately 116.33%. None of the given options match this answer, so there seems to be an error in the question or the options provided.
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Karishma expenditure and savings are in the ratio 5 : 3. Her income in...
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