## Percentage Questions and Answers Part-3

1. 80% of a number added to 80 gives the result as the number itself, then the number is :
a) 200
b) 300
c) 400
d) 480

Explanation: Let X be the number which is added to 80
80% of X = 0.8X
80 + 0.8X = X
0.2X = 80
X = $$\frac{{80}}{{0.2}} = 400$$

2. Reena goes to a shop to buy a radio costing Rs. 2568. The rate of sales tax is 7% and the final value is rounded off to the next higher integer. She tells the shopkeeper to reduce the price of the radio so that she has to pay Rs. 2568 inclusive of sales tax. Find the reduction needed in the price of the radio.
a) Rs. 180
b) Rs. 210
c) Rs. 168
d) Rs. 170

Explanation:
\eqalign{ & {\text{Reduction}} \cr & = {\frac{7}{{107}}} \times 2568 \cr & = 168 \cr}

3. Australia scored a total of X runs in 50 overs. India tied the scores in 20% less overs. If India's average run rate had been 33.33% higher the scores would have been tied 10 overs earlier. Find how many runs were scored by Australia?
a) 250
b) 240
c) 200
d) Can't be determined

Explanation: Run scored = Over × Run rate
If overs is reduced by 25%, run rate will go up by 33.33%. Hence, Australia could have scored any number of runs.

4. In 2000, the market shares of the toilet soaps Margo, Palmolive and dove were 40%, 30% and 30% respectively. Starting from the next year, a new soap enters into the market each year and gets 10% of the market share. The existing soap share the remaining market share in the same ratio as they did in the previous year. What percent of the total market share will mango have in 2002?
a) 28%
b) 32%
c) 32.4%
d) 34

Explanation: In 2000, the market share was 40%, 30% and 30%, means
the ratio is 4 : 3 : 3
In 2001, a new product (A) enters and has 10% market share, 90% of the remaining market is shared by the previous 3.
Now, divide 90% in the ratio 4 : 3 : 3 , i.e 36%, 27%, 27%.
Now the ratio is 36 : 27 : 27 : 10
In 2002, another new product (B) enters and has 10% market share, now the remaining 90% market share is distributed in the ratio,
36 : 27 : 27 : 10
and hence remaining 32.4%, 24.3%, 24.3%, 9%
Thus, the market share of Margo in 2002 is 32.4%

5. In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how many candidates applied for the examination?
a) 30000
b) 35000
c) 37000
d) 39000

Explanation:
\eqalign{ & {\text{Let the total number of applicants be x}}. \cr & {\text{Number of eligible candidates}} \cr & = {\text{ }}95\% {\text{ }}of{\text{ }}x \cr & {\text{Eligible candidates of other categories}}, \cr & = 15\% \,of\,\left( {95\% {\text{ }}of{\text{ }}x} \right) \cr & = {\frac{{15}}{{100}}} \times {\frac{{95}}{{100}}} \times x \cr & = \frac{{57}}{{400}}x \cr & or,\left( {\frac{{57}}{{400}}} \right)x \cr & x = \frac{{ {4275 \times 400} }}{{57}} \cr & \,\,\,\,\,\, = 30000 \cr}

6. In a class, the no. of boys is more than the no. of girls by 12% of the total strength. The ratio of boys and girls is:
a) 15 : 11
b) 11 : 14
c) 14 : 11
d) 8 : 11

Explanation: Let the no. of total student in the class = 100 and number of boy = X
and 12% of the 100 is 12
Number of girl is x - 12
Total number of student is x + (x - 12) = 100
So, x = 56
No of boys = 56
No. of girls = 44
Boys : Girls = 56 : 44 = 14 : 11

7. In an office there were initially N employees. The HR manager first hired P% employees then after a month Q% employees left the office, the value of (P - Q) is:
a) PQ
b) $$\frac{{{\text{PQ}}}}{{100}}$$
c) $$\frac{{\text{P}}}{{\text{Q}}}$$
d) $$\frac{{\text{Q}}}{{\text{P}}}$$

Explanation:
\eqalign{ & \frac{{\text{P}}}{{100 + {\text{P}}}} = \frac{{\text{Q}}}{{100}} \cr & 100\left( {{\text{P}} - {\text{Q}}} \right) = {\text{PQ}} \cr & \left( {{\text{P}} - {\text{Q}}} \right) = \frac{{{\text{PQ}}}}{{100}} \cr}

8. The amount of work in a leather factory is increased by 50%. By what percent is it necessary to increase the number of workers to complete the new amount of work in previously planned time, if the productivity of the new labour is 25% more.
a) 60%
b) 66.66%
c) 40%
d) 33.33%

Explanation: Men × Time = Work
100 × 1 = 100 unit work
150 × 1 = 150 unit work
Extra man power = 50
But, new workers are $$\frac{5}{4}$$ time as efficient as existing workers
So, Actual no. of workers = $$\frac{{50}}{{\frac{5}{4}}}$$ = 40 workers
% required = $$\frac{{40 \times 100}}{{100}} = 40\%$$

9. A big cube is formed by rearranging the 160 coloured and 56 non-coloured similar cubes in such a way that the expouser of the coloured cubes to the outside is minimum. The percentage of exposed area that is coloured is:
a) 25.9%
b) 44.44%
c) 35%
d) 32%

Explanation: Total number of cubes = 160 + 56 = 216
Side of cube = 6 unit
No. of cubes without exposure = (6 - 2)3 = 64
Thus 64 cubes will be inside of a big cube
Now, rest cubes = 160 - 64 = 96
No. of cubes with one face outside = 6 × (4 × 4) = 96
Required % = $$\frac{{90 \times 100}}{{216}} = 44.44\%$$

10. 78% of 750 + 34% of x = 30% of 2630. Find x.
a) 960
b) 600
c) 800
d) 750

\eqalign{ & 78\% \,{\text{of}}\,\,750 + 34\% \,{\text{of}}\,x = 30\% \,{\text{of}}\,\,2630 \cr & {\frac{{ {78 \times 750} }}{{100}}} + \frac{{34x}}{{100}} = \left( {30 \times 2630} \right) \times 100 \cr & 78 \times 750 + 34x = 30 \times 2630 \cr & 34x = 78900 - 58500 \cr & x = \frac{{20400}}{{34}} \cr & x = 600 \cr}