## Percentage Questions and Answers Part-7

1. Heinz produces tomato puree by boiling tomato juice. Tomato puree has 20% water whereas tomato juice has 90% water.How many litres of tomato puree will be obtained from 20 litres of tomato juice ?
a) 2 litres
b) 3 litres
c) 2.5 litres
d) 5 litres

Explanation: 20 litres juice contain 10% Tomato, i.e.
20L juice = $$\frac{{20 \times 10}}{{100}}$$  = 2L Tomato
Tomato puree contains 80% of water and 20% tomato.
This 80% tomato = 2L (which is contained by 100 puree)
Now this 2 L Consist 80% in puree
Total puree will be $$\frac{2}{{0.8}} = 2.5{\text{L}}$$

2. What is the percentage change in the result when we add 50 to a certain number x, instead of subtracting 50 from the same number x?
a) 50 %
b) 75 %
c) 100 %
d) Can't be determined

Explanain : If we take different values of x then,
Let x = 150, then error%
\eqalign{ & = \frac{{ {\frac{{ {200 - 100} }}{{100}}} }}{{100}} \cr & = 100\% \cr}
Again if x = 100, then error%
\eqalign{ & = \frac{{ {\left( {150 - 50} \right) \times 100} }}{{100}} \cr & = 200\% \cr}
If we take different value of x, then we get different answer so we can't determine it.

3. In a school, there are 100 students. 60% of the students are boys, 40% of whom play hockey and the girls don't play hockey, 75% of girls play badminton. There are only two games to be played. The number of student who don't play any game is:
a) 10 %
b) 20 %
c) 36 %
d) Can't be determined

Explanation: Total student = 100
Boys = 60
Girls = 40
Boys who plays hockey = 40% = 24
Girls who plays Badminton = 75% = 30
No girls plays hockey.
Since, we do not have information that whether the rest of the boys are playing badminton or not. So, we cannot determine the total no. of student who don't play any game.

4. A book consist of 30 pages, 25 line on each page and 35 characters on each line. If this content is written in another note book consisting 30 lines and 28 characters per line then the required no. of pages will how much percent greater than previous pages?
a) 4.16%
b) 5%
c) 6.66%
d) 7%

Explanation:
\eqalign{ & {\text{Let the required number of pages be }}x. \cr & 30 \times 25 \times 35 = x \times 30 \times 28 \cr & x = 31.25 \approx 32 \cr & \% \,{\text{increase}}\,{\text{in}}\,{\text{number}}\,{\text{of}}\,{\text{pages}}, \cr & = {\frac{2}{{30}}} \times 100 \cr & = 6.66\% \cr}

5. A fraction in reduced form is such that when it is squared and then its numerator is increased by 25% and the denominator is reduced to 80% it results in $$\frac{5}{8}$$ of original fraction. The product of the numerator and denominator is
a) 6
b) 12
c) 10
d) 7

Explanation:
\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{fraction}}\,{\text{be}}\,\frac{{100x}}{{100y}} \cr & {\text{According}}\,{\text{to}}\,{\text{the}}\,{\text{question}}, \cr & {\left( {\frac{{100x}}{{100y}}} \right)^2} = \frac{{125{x^2}}}{{80{y^2}}} = \frac{{25{x^2}}}{{16{y^2}}} \cr & \frac{{25{x^2}}}{{16{y^2}}} = \frac{5}{8}\left( {\frac{{100x}}{{100y}}} \right) \cr & {\frac{{100x}}{{100y}}} = \frac{2}{5} \cr & {\text{product of numerator and denominator}} \cr & = 2 \times 5 = 10 \cr}

6. Mr. X salary increased by 20%. On the increase, the tax rate is 10% higher. The percentage increase in tax liability is:
a) 20 %
b) 22 %
c) 23 %
d) 24 %

Explanation: Let his original salary be Rs. 100
Salary after increment = Rs. 120
Let the tax on original salary be 20% and now tax on increased salary (Rs. 20) will be 22% i.e. Rs. 4.40
Increase in tax liability $$= \frac{{4.40}}{{20}} \times 100 = 22\%$$

7. The total emoluments of A and B are equal. However, A gets 65% of his basic salary as allowances and B gets 80% of his basic salary as allowances. What is the ratio of the basic salaries of A and B?
a) 16 : 13
b) 5 : 7
c) 12 : 11
d) 7 : 9

Explanation: Let the basic salaries of A and B be x and y respectively.
\eqalign{ & x + 65\% \,\,{\text{of }}x = y + 80\% \,\,{\text{of }}y \cr & x + \frac{{ {65x} }}{{100}} = y + \frac{{ {80y} }}{{100}} \cr & \frac{x}{y} = \frac{{180}}{{165}} \cr & x:y = 12:11 \cr}

8. Distance between A and B is 72 km. Two men started walking from A and B at the same time towards each other. The person who started from A traveled uniformly with average speed of 4 km/hr. The other man traveled with varying speed as follows: In the first hour his speed 2 km/hr, in the second hour it was 2.5 km/hr, in the third hour it was 3 km/hr, and so on. When/where will they meet each other?
a) 7 hours after starting
b) 10 hours after starting
c) 35 km from AMid-way between A and B
d) 50%

Explanation: They covered the distance in this way together in different hours
6 + 6.5 + 7 + 7.5 + 8 + 8.5 + 9 + 9.5 + 10 = 72 Means, they'll meet at the 9th hr.
So, In that time A will cover = 4 × 9 = 36km
They will meet in Midway

9. In company there are 75% skilled workers and reaming are unskilled. 80% of skilled workers and 20% of unskilled workers are permanent. If number of temporary workers is 126, then what is the number of total workers ?
a) 480
b) 510
c) 360
d) 377

Explanation:
\eqalign{ & {\text{Let the number of total workers}} = x \cr & {\text{Number of skilled workers}} \cr & = 75\% \,of\,x = \frac{{75x}}{{100}} = \frac{{3x}}{4} \cr & {\text{No}}{\text{. of unskilled workers}} \cr & = 25\% \,of\,x = \frac{{25x}}{{100}} = \frac{x}{4} \cr & {\text{No}}{\text{. of permanent workers}}, \cr & = {\frac{{80}}{{100}}} \times {\frac{{3x}}{4}} + {\frac{{20}}{{100}}} \times {\frac{x}{4}} \cr & = {\frac{{3x}}{5}} + {\frac{x}{{20}}} \cr & = \frac{{13x}}{{20}} \cr & {\text{No}}{\text{.}}\,{\text{of}}\,{\text{temporary}}\,{\text{workers}} = \cr & x - {\frac{{13x}}{{20}}} = \frac{{7x}}{{20}} \cr & \frac{{7x}}{{20}} = 126 \cr & x = 360 \cr}

10. Population of a district is 2,96,000 out of which 1,66,000 are male. 50% of the population is literate. If 70% males are literate, then the number of woman who are literate, is
a) 32,200
b) 31,800
c) 66,400
d) 48,000