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Question 1: If the price of sugar is raised by 25%, find by how much percent a householder must reduce his consumption of sugar so as not to increase his expenditure ?

(a) 10%
(b) 20%
(c) 18%
(d) 25%

Percent decrease = {a/(100+a)} x 100%

Here, a = 25%

So, {25 /(100 + 25)} x 100 = (25/125) x 100 = 20%

Question 2: The price of an article has been reduced by 25%. In order to restore the original price, the new price must be increased by

Percentage increase in price = {a/(100-a)} x 100%

Here, a = 25%

So required increase = {25 /(100 – 25)} x 100 = 100/3%

Question 3: If the duty on an article is reduced by 40% of its present rate, by how much percent must its consumption increase in order that the revenue remains unaltered ?

Required increase percent = {a/(100-a)} x 100%

Here, a = 40%

So the required percentage increase is:

{40/(100-40)} x 100

= (40/60) x 100

200/3%

Question 4: If the price of a commodity is decreased by 20% and its consumption is increased by 20%, what will be the increase or decrease in the expenditure on the commodity?

(a) 4% increase
(b) 4% decrease
(c) 8% increase
(d) 8% decrease

Let the CP of each article = Rs. 100

Consumption = 100 units

Initial expenditure = Rs. (100 × 100) = Rs. 10000

New price of article = Rs. 80

Consumption = 120 units

Expenditure = Rs. (120 × 80)= Rs. 9600

Decrease = Rs. (10000 – 9600) = Rs. 400

∴ Percentage decrease = {(400 x 100)/ 10000} = -4%

Alternate Method:

Here, the price is decreased by 20% and the consumption is increased by 20%.

So, the net change in expenditure

= {x – y – (xy /100)}

= {20 – 20 – (400/100 )} = -4%

Hence, the expenditure decreased by 4%.

Question 5: If the price of petrol be raised by 20%, then the percentage by which a car owner must reduce his consumption so as not to increase his expenditure on petrol is

Percentage decrease in the consumption of petrol

Here, a = 20%

Hence, the required percentage decrease

= [{20 /(100 + 20 )} x 100]% = 50/3%