CAT 2024 Percentage Questions: According to the CAT syllabus 2024, the exam includes approximately 4-5% of percentage questions from the CAT 2024 Quantitative Aptitude syllabus. There is a significant emphasis on the use of percentages across all chapters of commercial arithmetic, indicating their overall importance, particularly in topics such as Profit and Loss, Ratio and Proportion, Time and Work, and Time, Speed, and Distance.

Percentage questions for CAT appear in the Arithmetic section and are usually of moderate difficulty. There are various types of CAT Percentage Questions like percentage increase /decrease, change of base and applications based on Percentage

Also Read: CAT 2024 Preparation Tips for Beginners

CAT 2024 Percentage Formula

A crucial aspect of CAT Preparation involves being familiar with all the important formulas for CAT 2024. In this article, we will focus on percentages and provide the formula for calculating percentages below:

Also Read: CAT 2024 Quant Practice Questions with Answers

15+ CAT 2024 Percentage Questions

Moving on, given below are some of the top and most-asked CAT questions on percentage. Check them out to score well on the topic:

Question: If 16% of 40% of a number is 8, then find the number.

Answer: 125

Solution:

Let X be the required number.

Therefore, as per the given question, 

(16/100) × (40/100) × X = 8

So, X = (8 × 100 × 100) / (16 × 40) = 125

Question: A container contains 175 millilitres of water and 700 millilitres of alcohol. Gopal removes 10% of the mélange and replaces it with the same volume of water. The procedure is performed again. What is the current proportion of water in the mixture?

1. 22.6
2. 35.2
3. 45.4
4. 20.5

Answer: B

Solution: 

Final quantity of Alcohol in the mixture= (700/(700+175) x (90/100)2x(700+175) = 567ml
So, the final volume of water in the mixture = 875-567=308ml
Hence, the water percentage in the mixture = (308/875) x 100= 35.2%

Question: Out of two numbers, 40% of the greater number is equal to 60% of the smaller. If the sum of the numbers is 150, then the greater number is?

Answer: 90

Solution:

Let X be the greater number. Therefore, Smaller number = 150 – X {given that the sum of two numbers is 150}

According to the question,

• (40 × X)/100 = 60(150 – X)/100
• 2p = 3 × 150 – 3X
• 5X = 3 × 150
• X = 90

Question: The tensile strength of a substance A is a multiple of the quantities of a, b, c, and d used. What will be the overall change in A's tensile strength if the amounts of material a, b, c, and d are altered by 30%, -30%, -25%, and 25%, respectively?

1. No Change
2. +14.68%
3. –14.68%
4. Depends on the initial amount of a, b, c, d

Answer: C

Solution:

Since, the tensile strength of A = a * b * c * d, If we assume initial tensile strength to be 100, we can apply successive % changes to arrive at the final figure

100 -30% ---> 70

70 + 30% ---> 91

91 + 25% ---> 113.75

113.75 – 25% --> ~85.31

Percentage change in tensile strength = -14.68%

The overall change in tensile strength of A will be -14.68%.

Hence, the answer is -14.68%.

Question: If M = y% of z and N = z% of y, then which of the following must be true?

1. M is lesser than N.
2. M is more than N
3. The relation between M and N cannot be determined.
4. None of these

Answer: Option D

Solution:

y% of z = (y/100 x z) = (z/100 x y) = z% of y | M = N.

Question: In a tournament, a team has played 40 matches so far and won 30% of them. If they win 60% of the remaining matches, their overall win percentage will be 50%. Suppose they win 90% of the remaining matches, then the total number of matches won by the team in the tournament will be: 

1. 84
2. 69
3. 76
4. 90

Answer: 84

Question: Two alcohol solutions, A and B, are mixed in the proportion 1:3 by volume. The volume of the mixture is then doubled by adding solution A such that the resulting mixture has 72% alcohol. If solution A has 60% alcohol, then the percentage of alcohol in solution B is: 

1. 80 %
2. 92 %
3. 91 %
4. 79 %

Answer: 92% 

Questions: Meena scored 40% in an examination and after review, even though her score is increased by 50%, she failed by 35 marks. If her post-review score is increased by 20%, she will have 7 marks more than the passing score. The percentage score needed to pass the examination is

1. 46
2. 70
3. 45
4. 75

Answer: 70  

Question: In 2010, a library contained 11500 books in two categories – fiction and non-fiction. In 2015, the library contained 12760 books in these two categories. During this period, there was a 10% increase in the fiction category and a 12% increase in the non-fiction category. How many fiction books were in the library in 2015?

1. 5760
2. 6600
3. 1920
4. 1322

Answer: 6600

Question: The income of Amala is 20% more than that of Bimala and 20% less than Kamala's. If Kamala's income goes down by 4% and Bimala's goes up by 10%, then the percentage by which Kamala's income would exceed Bimala's is nearest to

1. 31
2. 29 
3. 28
4. 32 

Answer: 31

Solution:

Assuming the income of Bimla = 100a, then the income of Amala will be 120a. And the income of Kamala will be 120a*100/80=150a. If Kamala's income goes down by 4%, then the new income of Kamala = 150a-150a(4/100) = 150a-6a=144a. If Bimla's income goes up by 10 per cent, her new income will be 100a+100a(10/100)=110a. 

Hence Kamala income will exceed Bimla's income by (144a-110a)*100/110a=31. 

Question: Instead of a metre scale, a cloth merchant uses a faulty 120 cm scale while buying, but uses a faulty 80 cm scale while selling the same cloth. If he offers a discount of 20%, what is his overall profit percentage? 

• A 20% 
• B 25% 
• C 40% 
• D 15% 

Answer: A 

Solution: 

Let's say the cost of the cloth is x rs per metre. Because of the faulty meter, he is paying x for 120 cms when buying. So cost of 100 cms = 100x/120. 

He is selling 80 cms for x, so selling price of 100cms of cloth is 100x/80. discount = 20% (600( 99 − 100 1)) ÷ (600( 99 )) × 100 100 = 1 100 120 100 30 100 150 100 150+30+120 100 300 so the effective selling price is .8*100x/80= x profit = SP-CP= x - 100x/120 = x/6 Profit % = x/6 divided by 100x/120 = 20%

Question: Class B has 50% more students than class A. Number of girls in class A is equal to number of boys in class B. The percentage of girls is the same in both classes. What percentage of the student group are boys?

1. 33.33%
2. 40%
3. 45%
4. 55%

Answer: 40% 

Question: A man spent 40% of his monthly income on food items. Of the remaining amount, he spent 80% on E M.I. Now he saves 5/6 of the remaining amount and then he saves 78,600 yearly. Find the monthly income of a man. 

Solution: Let the monthly income of a man be 100x. Amount spent on food items = × 100x = 40x Amount spent of E.M.I. = × (100x – 40x) = × 60x = 48x Remaining amount = 60x – 48 = 12x Amount saved by man = × 12x = 10x Amount saved monthly = = Rs. 6550 ⸫ Using the data provided in the question, we get: 10x = 6550 Monthly income of man = 100x = Rs. 65500

Answer: 65500  

Question: The number of seats in a stadium is decreased by 15% and also the price of the ticket is increased by 20%. What is the effect on the revenue collected?

Answer: 2% increase
Solution: 

Let the number of seats in the stadium initially be 100.

Let the price of each ticket initially be Rs. 10.

Initial revenue of the stadium = 100 × 10 = Rs. 1000

New number of seats in the stadium = 85% of 100 = 85

New price of each ticket = 120% of 10 = Rs. 12

New revenue of the stadium = 85 × 12 = Rs. 1020

Increase in revenue of stadium = 1020 – 1000 = Rs. 20

Percent increase in revenue of the stadium = (20/1000) × 100 = 2%

Also Read: Important Topics for CAT 2024

Question: The total salary of A and B is Rs 60,000. If the salary of A increases by 8% and the salary of B increases by 6%, then their total salary would increase to Rs 64,100. Find the salary of B

Answer: Rs 35000

Solution: Let the salary of B be x.

So, the salary of A = 60000 – x

Therefore, According to the question:

8% of A’s salary + 6% of B’s salary = 64100 – 60000

1. × (60000 – x) + × x = 4100
2. 480000 – 8x + 6x = 410000
3. 2x = 480000 – 410000
4. x = Rs. 35000

Question: If the length of a rectangle is increased by 16% and its breadth is decreased by 25%, find the percentage decrease in the area of the rectangle.

Answer: 13%

Solution: Let the original length and breadth of the rectangle be 100 units and 40 units respectively.

Increased length = 100 × = 116 units

Decreased breadth = 40 × = 30 units

Area decreased by = (100 × 40) – (116 × 30) = 520 square units

Required percentage = × 100% = 13%

Question: 64% of a bigger number is 6 more than 75% of a smaller number. The bigger number is 140 more than the smaller one. What is the sum of both numbers?

Solution: Let the smaller number be x, then

The bigger number = (x + 140)

According to the question

(x + 140) × 64% – x × 75% = 6

0.64x + 89.6 – 0.75x = 6

x = 760

Required sum = Smaller number + Bigger number = x + (x + 140) = 760 + 900 = 1660

Answer: 1660

Also Read | CAT Predicted Question Paper 2024

Tips to Solve CAT 2024 Percentage Questions

Percentages can be quickly calculated using these shortcuts in a variety of situations. To use these shortcuts effectively, you have to understand the percentage formula mentioned above properly and how to adjust them according to the scenario.

A number's percentage increase or decrease can be calculated using this formula: (new value - old value)/old value x 100 = percentage increase/decrease. 

Eg: An increase of 20% would be calculated as (120 - 100) / 100 x 100 = 20 x 100 = 20 x 100 = 20%.

A number that is greater or less than another number can be calculated using the formula: (number/reference number) x 100 = percentage. 

Eg: if we have many 10 and a reference number of 100, the percentage is: (10/100) x 100 = 10%. Whenever the number exceeds the reference number (e.g. 120), the percentage will be greater than 100%, and when it is less than the reference number (e.g. 80), the percentage will be less than 100%.

Converting Percent to Decimal: Shift the decimal point two places to the left. For instance, 42% can be expressed as 0.42.

Converting Decimal to Percent: Shift the decimal point two places to the right. For example, 1.6 becomes 160%.

Converting Percent to Fraction: Place the per cent number as the numerator and 100 as the denominator, then simplify the fraction. For example, 42% becomes 42/100, which simplifies to 21/50.

Converting Fraction to Percent: First convert the fraction to a decimal, and then apply the steps for converting from decimal to percent. For example, 5/6 converts to 0.833 recurring, which then becomes 83 and 1/3%.

Appearing for an exam like CAT is a significant challenge, but it's important to remember that not performing well is not the end of the world. Countless other opportunities are waiting for you to explore. All the best!

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