3. The price of sugar is increased by 40%. By how much kg of consumption is decreased so as expenditure will increased by 10% only when he originally consumed 210 kg sugar.
Answers
Answer:
Shortcut Trick
If the price of commodities increased by r%, then the reduction in consumption, so as not to increase the expenditure = {r/(r + 100)} × 100%
Here, r = 40%
So, the reduction% in commodity = {40/(100 + 40)} × 100%
⇒ (40/140) × 100% = (2/7) × 100% = 28.57%
∴ The approximate percentage decrease in the consumption of sugar should be 29%
Traditional method:
Given:
The price of sugar increased by 40%
Calculation:
Let the initial consumption of sugar be x kg
Let the initial price be y Rs./kg
So, the total expenditure = Rs.xy
When the price increases by 40%, the new price = [(100 + 40)/100] × y = 1.4y Rs./kg
To keep the total expenditure of Rs.xy, the amount of sugar that can be purchased will be obtained as:
xy/1.4y = (1/1.4)x = x/1.4
So, the percentage decrease in sugar consumption = {[x - (x/1.4)]/x} × 100 = 28.57%
∴ The approximate percentage decrease in the consumption of sugar should be 29%
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Answer:
If the price of commodities increased by r%, then the reduction in consumption, so as not to increase the expenditure = {r/(r + 100)} × 100%
Here, r = 40%
So, the reduction% in commodity = {40/(100 + 40)} × 100%
⇒ (40/140) × 100% = (2/7) × 100% = 28.57%
∴ The approximate percentage decrease in the consumption of sugar should be 29%
Traditional method:
Given:
The price of sugar increased by 40%
Calculation:
Let the initial consumption of sugar be x kg
Let the initial price be y Rs./kg
So, the total expenditure = Rs.xy
When the price increases by 40%, the new price = [(100 + 40)/100] × y = 1.4y Rs./kg
To keep the total expenditure of Rs.xy, the amount of sugar that can be purchased will be obtained as:
xy/1.4y = (1/1.4)x = x/1.4
So, the percentage decrease in sugar consumption = {[x - (x/1.4)]/x} × 100 = 28.57%
∴ The approximate percentage decrease in the consumption of sugar should be 29