11. The price of a commodity rises from Rs. 10 per kg to 12.5 per kg. If the expenditure can not increase then find the percentage of reduction in consumption.
Sol:
% increase in price = \(\frac{{12.5 – 10}}{{10}} \times 100\)
= 25%
Explanation:
Firstly we have calculated % increase in price then converted it into its equivalent fraction \(\left( {\frac{1}{4}} \right)\)
Now let original price is 4 ⟹ it increases by 25% i.e. by 1 then new price will become 5.
price % consumption = expenditure
Hence to keep expenditure fixed ⟹ consumption is reduced from 5 to 4
so in both the cases expenditure will be 4 × 5 = 20
Now expenditure will be 5 ⟶ 4
∴ its equivalent percentage = \(\frac{{4 – 5}}{5} \times 100\) = – 20%
i.e. consumption should be decreased by 20%.
12. If length of a rectangle is increased by \(62\frac{1}{2}\)% and its breadth is decreased by 20%. Find the % change in area.
Sol:
Area = length × breadth
∴ % change in area = \(\frac{7}{{25}} \times 100\) = 28% Answer
13. If the side of a square is increased by 20% then find the percentage change in its area.
Sol:
20% = \(\frac{1}{5}\)
14. The sale of a cinema ticket is increased by \(16\frac{2}{3}\)% and the price of ticket is increased by \(14\frac{2}{7}\)%. Find the percentage change in revenue.
Sol:
15. If one side of a rectangle is increased by \(37\frac{1}{2}\)% and the otherside is decreased by 10%. Find the % change in its area.
Sol:
16. Two numbers are respectively 10% and 20% more than a third number. What percentage is the first of the second.
Sol:
∴ required % = \(\frac{{110}}{{120}} \times 100\)
= \(91\frac{2}{3}\)%
17. The price of wheat is increased by 40%. If the expenditure on wheat has to be kept the same as earlier. Find the ratio between the reduction in consumption and the original consumption.
Sol:
18. A reduction in the price of apples a person to purchase 3 apples for Rs. 1 instead of Rs. 1.25. What is the % of reduction in price ?
Sol:
∴ % decrease = \(\frac{{0.25}}{{1.25}} \times 100\)
= 20% Answer
19. A number is first reduced by 20% and then it is increased by 80%. what is the net effect of this change ?
Sol:
20. Two numbers are respectively 10% and 5% less than a third number. what percentage is the first number of the second ?
Sol:
10% = \(\frac{{10}}{{100}}\)
5% = \(\frac{{5}}{{100}}\)