Percentages 1/5

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25. Water tax is increased by 20% but its consumption is decreased by 20%. Then, the increase or decrease in the expenditure of the money is :
a. No change
b. 5% decrease
c. 4% increase
d. 4% decrease

Answer: D

Explanation:
Let tax = Rs.100 and
Consumption = 100 units
Original expenditure = Rs.$(100 \times 100) = Rs.10000$
New expenditure = Rs.$(120 \times 80) = Rs.9600$
Decrease in expenditure
= $\left( {\displaystyle\frac{{400}}{{10000}} \times 100} \right)\% = 4\% $

26. The price of sugar is increased by 20%. If the expenditure is not allowed to increase, the ratio between the reduction in consumption and the original consumption is :
a. 1:3
b. 1:4
c. 1:6
d. 1:5

Answer: C

Explanation:
Reduction in consumption
= $\left( {\displaystyle\frac{{20}}{{120}} \times 100} \right)\% = \displaystyle\frac{{50}}{3}\% $
$\displaystyle\frac{{{\rm\text{Reduction in consumption}}}}{{{\rm\text{Original consumption}}}}{\rm{ = }}\left( {\displaystyle\frac{{{\rm{50}}}}{{\rm{3}}}{\rm{ \times }}\displaystyle\frac{{\rm{1}}}{{{\rm{100}}}}} \right)$
= $\displaystyle\frac{1}{6} = 1:6$

27. The price of cooking oil has increased by 25% . The percentage of reduction that a family should effect in the use of cooking oil so as not to increase the expenditure on this account is :
a. 15%
b. 20%
c. 25%
d. 30%

Answer: B

Explanation:
Reduction in consumption:
=$\left( {\displaystyle\frac{{25}}{{125}} \times 100} \right)$%=20%

28. What will be 80 percent of a number whose 200 percent is 90 ?
a. 144
b. 72
c. 36
d. None of these

Answer: C

Explanation:
200% of x = 90 $ \Rightarrow x = \displaystyle\frac{{90 \times 100}}{{200}} = 45$
80% of x = $\left( {\displaystyle\frac{{80}}{{100}} \times 45} \right) = 36$

29. In an election between two candidates, the candidates who gets 30% of the votes polled is defeated by 15000 votes. The number of votes polled by the winning candidate is :
a. 11250
b. 15000
c. 26250
d. 37500

Answer: C

Explanation:
Let the votes polled by the winning candidate be x, then loosing candidates gets x - 15000.
(x - 15000) = 30% of (x + (x - 15000))
$\left( {x - 15000} \right) = \dfrac{3}{{10}}\left( {2x - 15000} \right)$
10x - 150000 = 6x - 45000
4x = 105000
x = 26250

30. In a college election, a candidate secured 62% of the votes and is elected by a majority of 144 votes. The total number of votes polled is :
a. 600
b. 800
c. 925
d. 1200

Answer: A

Explanation:
If winner gets 62%, then the loser gets (100 - 62) = 38% of votes. But given that winner got 144 votes more than loser.
(62% of x - 38% of x ) = 144
24% of x = 144
x = $\displaystyle\frac{{144 \times 100}}{{24}} = 600$

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Formulas Percentages Exercise Percentages: Exercise - 2