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%
Answers and Explanations
Answers: (b)
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
Answers and Explanations
Answers: (c)
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 ?
Answers and Explanations
Answers: (d)
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
Answers and Explanations
Answers: (b)
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
Answers and Explanations
Answers:(b)
Percentage decrease in the consumption of petrol
Here, a = 20%
Hence, the required percentage decrease
= [{20 /(100 + 20 )} x 100]% = 50/3%
Percentages: The Complete Lesson
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