# Percentage - Excercise 1

## Questions

1.   Entry fee in an exhibition was Rs. 1. Later, this was reduced by 25% which increased the sale by 20%. The percentage increase in the number of visitors is :

• 20.00%
• 40.00%
• 60.00%
• 80.00%

Let the total original sale be Rs. 100.
Then, original number of visitors = 100.
New number of visitors = ${\frac{120}{0.75}}$ = 160.
Increase %= 60%

2.   Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes or 35 small cakes per hour. The kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed. How many helpers are required?

• 10
• 15
• 20
• 25

20 large cakes will require the equivalent of 10 helpers working for one hour.
700 small cakes will require the equivalent of 20 helpers working for one hour.
This means if only one hour were available we would need 30 helpers.
But since three hours are available we can use 10 helpers.

3.   The current birth rate per thousand is 32, whereas corresponding death rate is 11 per thousand. The net growth rate in terms of population increase in percent is given by :

• 1.20%
• 2.10%
• 3.10%
• 1.30%

Net growth on= ${1000=(32-11)\frac{}{}}$= 21
. Net growth on =${\left(100=\begin{array}{c}\frac{21}{1000}\times100\end{array}\right)}$= 2.1%.

4.   The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 20 per cent. The two reductions together are equal to a single reduction of

• 45.00%
• 40.00%
• 35.00%
• 32.50%

Let the original price of the cycle be 100.
After the first reduction the price will be 75.
This new price is then reduced by ${\frac{20}{100}=0.8\times75}$
60 represents a reduction of 40 percent on the original.

5.   If the price of sugar rises from Rs. 6 per kg to Rs. 7.50 per kg, a person, to have no increase in his expenditure on sugar, will have to reduce his consumption of sugar by

• 15
• 20
• 25
• 30

Let original consumption = 100 kg and new consumption = x kg,
So, $(100\times6)=(x\times7.50)$
=x =80 kg
Reduction in consumption = 20%

6.   An agent, gets a commission of 2.5% on the sales of cloth. If on a certain day, he gets Rs. 12.50 as commission, the cloth sold through him on that day is worth

• 300
• 500
• 700
• 900

Let the total sale be Rs. x
Then 2.5%. of x =12.50
=(25/10$\times$1/100$\times$x) = 125/10
x = 500

7.   A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ? • 0.75D • 0.76D • 0.765D • None of the above The Correct answer is :0.765D If the price is reduced by 15 %, then the new price will be 0.85D nIf this new price is further reduced by 10% The discounted price will be=${(0.9\times0.85D)\frac{}{}}$= 0.765D 8. What percent decrease in salaries would exactly cancel out the 20 percent increase ? • (16 + 2/3) % • (15 + 2/3)% • (14 +1/3)% • (13 + 4/5)% The Correct answer is :(16 + 2/3) % Let the orginal salary = Rs. 100. New's salary = Rs.120. Decrease on 120 = 20. Decrease on 100 =(20/120$\times$100) = 16+2/3 9. The difference of two numbers is 20% of the larger number, if the smaller number is 20, then the larger number is : • 15 • 25 • 35 • 45 The Correct answer is :25 Let the large number be x. nThen${(x-20)=\frac{20x}{100}}{x-\frac{x}{5}}$= 20 x = 25. 10. To a sugar solution of 3 litres containing 40% sugar, one litre of water is added. The percentage of sugar in the new solution is : • 20 • 30 • 40 • 50 The Correct answer is :30 Quantity of sugar =${\left(\begin{array}{c}\frac{40}{100}\times3\end{array}\right)}$kg = 1.2 kg. New percentage =${\left(\begin{array}{c}\frac{1.2}{4}\times100\end{array}\right)}$= 30%. 11. In an examination, 34% of the students failed in Mathematics and 42% failed in English. If 20% of the students failed in both the subjects, then the percentage of students who passed in both the subjects was : • 34.00% • 44.00% • 54.00% • 64.00% The Correct answer is :44.00% Failed in mathematics, n(A) = 34 Failed in English, n(B) = 42 n(A∪B)=n(A)+n(B)−n(A∩B)=34+42−20=56 Failed in either or both subjects are 56 Percentage passed = (100−56)%=44% 12. How many litres of pure acid are there in 8 litres of a 20% solution ? • 1.4 • 1.5 • 1.6 • 1.7 The Correct answer is :1.6 Quantity of pure acid =${\left(\begin{array}{c}\frac{20}{100}\times8\end{array}\right)}$= 1.6 litres. 13. Ramesh started a software business by investing Rs. 50,000. After six months, Rajesh joined him with a capital of Rs. 75,000. After 3 years, they earned a profit of Rs. 27,000. What was Rajesh's share in the profit? • 10000 • 15000 • 20000 • 25000 The Correct answer is :15000 Ramesh : Rajesh =(50000 * 36):(25000 * 30)=4 : 5. Therefore, Rajesh's share Rs=(27000 * 5/9) =Rs.15,000. 14. In an election only two candidates contested 20% of the voters did not vote and 120 votes were declared as invalid. The winner got 200 votes more than his opponent thus he secured 41% votes of the total voters on the voter list. Percentage votes of the defeated candidate out of the total votes casted is: • 47.50% • 41.00% • 38.00% • 45.00% The Correct answer is :45.00% Let there be x voters and k votes goes to loser then 0.8x - 120 = k + (k + 200) k+200 = 0.41x k = 1440 and (k + 200) =1640 Therefore${(1440)\times(3200)\times(100)\frac{}{}}\$ = 45%

15.   600 students took the test on physics and chemistry. 35% students failed in physics and 45% students failed in chemistry and 40% of those who passed in chemistry also passed in physics, then how many students failed in both:

• 162
• 138
• 60
• None of these
The Correct answer is :None of these

Physics =>Failed= 35% Passed => 65%
Chemistry=>Failed=45%=> Passed=55%
Passed in both = 22% of total student
Percentage of students who are passed in any of the physics or chemistry or both =(65+55) - 22 = 98%
>So, the percentage of students who are failed in both = 2%
Therefore, total failed (in both subjects) students = 12