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19. The price of an article has been reduced by 25%. In order to restore the original price, the new price must be increased by :
a. $33\displaystyle\frac{1}{3}$%
b. $11\displaystyle\frac{1}{9}$%
c. $9\displaystyle\frac{1}{{11}}$%
d. $66\displaystyle\frac{2}{3}$%

Answer: A

Explanation:
Let original price = Rs.100
Reduced price = Rs.75
Increase on Rs.75 = Rs.25
Increase on Rs.100 = $\left( {\displaystyle\frac{{25}}{{75}} \times 100} \right)\% = 33\displaystyle\frac{1}{3}\% $

20. p is six times as large as q. The percent that q is less than p is :
a. $83\displaystyle\frac{1}{3}$
b. $16\displaystyle\frac{2}{3}$
c. 90
d. 60

Answer: A

Explanation:
p = 6q. Then q is less than p by 5q.
q is less than p by $\left( {\displaystyle\frac{{5q}}{{6q}} \times 100} \right)\% = 83\displaystyle\frac{1}{3}\% $

21. Sameer spends 40% of his salary on food articles and $\displaystyle\frac{1}{3}rd$ of the remaining on transport. If he saves Rs.450 per month which is half of the balance after spending on food items and transport, what is his monthly salary?
a. Rs.1125
b. Rs.2250
c. Rs.2500
d. Rs.4500

Answer: B

Explanation:
Suppose, salary = Rs.100
Expenditure on food = Rs.40
Balance = Rs.60
Expenditure on transport
= $\displaystyle\frac{1}{3} \times 60$ = Rs.20
Now balance = Rs.40
Saving = Rs.20
If saving is 20, salary = Rs.100
If saving is 450,
salary = Rs.$\left( {\displaystyle\frac{{100}}{{20}} \times 450} \right) = Rs.2250$

22. The population of a town increases 4% annually but is decreased by emigration annually to the extent of (1/2)% .What will be the increase percent in three years ?
a. 9.8
b. 10
c. 10.5
d. 10.8

Answer: D

Explanation:
Increase in population 4% and reduction due to emigration (1/2)%. So net percentage increase = 4 - (1/2)% = 3 1/2% = (7/2)%
Increase in 3 years over 100
= $100 \times {\left( {1 + \displaystyle\frac{7}{{200}}} \right)^3}$
= $\left( {100 \times \displaystyle\frac{{207}}{{200}} \times \displaystyle\frac{{207}}{{200}} \times \displaystyle\frac{{207}}{{200}}} \right)$
= $\displaystyle\frac{{{{(200 + 7)}^3}}}{{80000}}$
= $\displaystyle\frac{{{{(200)}^3} + {{(7)}^3} + 4200(200 + 7)}}{{80000}}$
= $\displaystyle\frac{{8869743}}{{80000}} = 110.8718$
Increase % = 10.8%

23. A man's basic pay for a 40 hour week is Rs.20. Overtime is paid for at 25% above the basic rate. In a certain week he worked overtime and his total wage was Rs.25. He therefore worked for a total of :
a. 45 hours
b. 47 hours
c. 48 hours
d. 50 hours

Answer: C

Explanation:
Basic rate per hour = Rs.$\left( {\displaystyle\frac{{20}}{{40}}} \right) = $ Rs.$\displaystyle\frac{1}{2}$
Overtime per hour = 125% of Rs.$\displaystyle\frac{1}{2}$=$\displaystyle\frac{{125}}{{100}} \times \frac{1}{2}$=Rs.$\displaystyle\frac{5}{8}$
Suppose he worked x hours overtime.
Then,$20 + \displaystyle\frac{5}{8}x = 25$ or $\displaystyle\frac{5}{8}x = 5$
x = $\displaystyle\frac{{5 \times 8}}{5} = 8$ hours
So he worked in all for (40+8) hours = 48 hours.

24. On decreasing the price of T.V.sets by 30% , its sale is increased by 20%. What is the effect on the revenue received by the shopkeeper ?
a. 10% increase
b. 10% decrease
c. 16% increase
d. 16% decrease

Answer: D

Explanation:
Let, price = Rs.100, sale = 100
Then, sale value = Rs.$(100 \times 100)$=Rs.10000
New sale value = Rs.$(70 \times 120) = Rs.8400$
Decrease % = $\left( {\displaystyle\frac{{1600}}{{10000}} \times 100} \right)\% = 16\% $

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Formulas Percentages Exercise Percentages: Exercise - 2