9. Sum of 5% of a number and 9% of other number is equal to sum of 8% of first number and 7% of the second number. Find ratio between the numbers.
a. 1 : 2
b. 2 : 3
c. 3 : 2
d. 9: 13

Answer: B

Explanation:
Let the numbers are x and y.
Then 5% of x + 9% of y = 8% of x + 7% of y
⇒ 3% of x = 2% of y
⇒ $\left( {\dfrac{3}{{100}}} \right)x = \left( {\dfrac{2}{{100}}} \right)y$
⇒ $\dfrac{x}{y} = \dfrac{2}{3}$
⇒ x : y = 2 : 3

10. A man spends 10% of his income on food and 80% of the remaining income on clothing. If he still has a balance of Rs. 180. what is his total income?
a. 1000
b. 1200
c. 1300
d. 1400

Answer: C

Explanation:
Total Income = 180 x $\displaystyle\frac{{{\rm{100}}}}{{{\rm{100 - 10}}}}{\rm{ \times }}\displaystyle\frac{{{\rm{100}}}}{{{\rm{100 - 80}}}}$
= 180 x $\displaystyle\frac{{{\rm{100}}}}{{{\rm{90}}}}{\rm{ \times }}\frac{{{\rm{100}}}}{{{\rm{20}}}}$ = Rs. 1000

11. The length of a rectangle is increased by 60%. By what percent would be width have to be decreased to maintain the same area ?
a. $37\displaystyle\frac{1}{2}$ %
b. 60%
c. 75%
d. None of these

Answer: A

Explanation:
Let length = 100 m, breadth = 100 m
New length = 160 m, new breadth = x m
Then $160 \times x = 100 \times 100$
or $x = \displaystyle\frac{{100 \times 100}}{{160}} = \displaystyle\frac{{125}}{2}$
Decrease in breadth = $\left( {100 - \displaystyle\frac{{125}}{2}} \right)\% = 37\displaystyle\frac{1}{{2 }}%$

12. If the side of a square is increased by 30% , its area is increased by :
a. 9%
b. 30%
c. 60%
d. 69%

Answer: D

Explanation:
Let, side = 100 cm
Area = ${(100 \times 100)}$$\,c{m^2}$ = $10000\, c{m^2}$
New area = ${(130 \times 130)}$$\,c{m^2}$ = $16900\,c{m^2}$
Increase in area = $\left( {\displaystyle\frac{{6900}}{{10000}} \times 100} \right)\% = 69\% $

13. 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}\% $

14. 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}\% $

15. 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.$\left( {\displaystyle\frac{{100}}{{20}} \times 450} \right) = Rs.2250$

16. 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%