# Percentages Questions for CAT

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Percentages questions for CAT PDF covers some important percentages questions appeared in CAT papers. In CAT, percentages is not a stand alone topic, it goes along with ratios, proportions, profit and loss topics. The difficulty of questions asked from Percentages in CAT exam will be from easy to moderate.

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You can download the Percentages Questions for CAT PDF or you can go through the details below. This questions and answers are from the previous CAT papers.

Percentages Questions for CAT Questions with answers:

Question 1:

If equal numbers of people are born on each day, find the approximate percentage of the people whose birthday will fall on 29th February. If we are to consider people born in 20th century (1901-2000) and assuming no deaths.

A. 0.374

B. 0.5732

C. 0.0664

D. None of these

Question 2:

Forty percent of the employees of a certain company are men, and 75 percent of the men earn more than Rs. 25,000 per year. If 45 percent of the company’s employees earn more than Rs. 25,000 per year, what fraction of the women employed by the company earn Rs. 25,000 year or less’?

A. 2/11

B. 1/4

C. 1/3

D. 3/4

Question 3:

After allowing a discount of 11.11%, a trader still makes a gain of 14.28%. At how many percentage above the cost price does he mark on his goods?

A. 28.56%

B. 35%

C. 22.22%

D. None of these

Question 4:

The price of a Maruti car rises by 30% while the sales of the car come down by 20%. What is the percentage change in the total revenue?

A. –4%

B. –2%

C. +4%

D. +2%

Question 5:

I sold two watches for Rs. 300 each, one at the loss of 10% and the other at the profit of 10%. What is the percentage of loss(–) or profit(+) that resulted from the transaction?

A. (+)10

B. (–)1

C. (+)1

D. (–)10

Solutions for CAT Percentages Questions:

In 20th century, 1901-2000, or in 100 years total people born will be = $365 \times 100 \times 1 + 25 \times 1$
And people born on 29th february = $25 \times 1$ (25 days date will be 29 feb. in 100 years)
Hence percentage will be = $\frac{25 \times 1}{365 \times 100 \times 1 + 25 \times 1} \times 100$ = 0.0684

Let the number of employees be 100.
=> 40 men and 60 women.
Number of men getting more than 25000 = 30
Number of people getting more than 25000 = 45
Number of women getting more than 25000 = 45 – 30 = 15
Fraction of women getting less than 25000 = $\frac{45}{60}$ = $\frac{3}{4}$

Let’s say cost price is 100
gain = 14.28
selling price = 114.28
Marked price = x(say)
So $x- \frac{11.11x}{100} = \frac{8x}{9} = 114.28$
Or $x = 128.52$
So marked price is 28.52% more than cost price.

let’s say price of maruti car is x rs.
Sales = y
revenue = xy
Changed price = 1.3x
changed value of sales = 0.8y
new revenue = 1.04 xy
Percentage change in revenue = 4%

Selling price of first watch = 300
Profit = 10%
cost price = $\frac{300}{1.1}$
Selling price of second watch = 300
Loss = 10%
cost price = $\frac{300}{0.9}$
Total selling price of transaction= 600
Total cost price of transaction = $300(\frac{10}{11} + \frac{10}{9}) = 600 (\frac{100}{99})$
Loss = $600 (\frac{100}{99} – 1)$
%loss = $(600 (\frac{100}{99} – 1)) \div (600(\frac{100}{99})) \times 100 = 1$

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