**The percentages **is one of the important topics in the **CAT ****Quants (Arithmetic) **section. These questions are not very tough, and hence you should not miss out on the questions from Percentages. Firstly, understand the concept of **Percentages, including all the Important Formulas**. Solve & practice more questions from CAT Percentage so that you can easily solve these questions in the exam. You can check out these CAT Percentages-based questions from the **CAT Previous year’s papers**. In this post, we will look into some important Percentage Questions for CAT. These are a good source of practice for CAT preparation; If you want to practice these questions, you can download these Important **CAT Percentage Questions** (with detailed answers) **PDF** along with the video solutions below, which is completely Free.

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**Question 1:Â **At the end of year 1998, Shepard bought nine dozen goats. Henceforth, every year he added p% of the goats at the beginning of the year and sold q% of the goats at the end of the year where p > 0 and q > 0. If Shepard had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true?

[CAT 2003 leaked]

a)Â p = q

b)Â p < q

c)Â p > q

d)Â p = q/2

**1)Â AnswerÂ (C)**

**Solution:**

By the end of the year 2002, Shepard bought 4 times and sold 4 times. He is left with the initial number of goats that he had in 1998. If the percentage of goats bought is equal to or lesser than the percentage of goats sold, then there would be a net decrease in the total number of goats. For the number of goats to remain the same, p has to be greater than q, because p% is being calculated in a lesser number and q% is being calculated on a greater number. Hence, p > q.

**Question 2:Â **Arun’s present age in years is 40% of Barun’s. In another few years, Arun’s age will be half of Barun’s. By what percentage will Barun’s age increase during this period?

**2)Â Answer:Â 20**

**Solution:**

Let Arun’s current age be A. Hence, Barun’s current age is 2.5A

Let Arun’s age be half of Barun’s age after X years.

Therefore, 2*(X+A) = 2.5A + X

Or, X = 0.5A

Hence, Barun’s age increased by 0.5A/2.5A = 20%

**Question 3:Â **The strength of an indigo solution in percentage is equal to the amount of indigo in grams per 100 cc of water. Two 800 cc bottles are filled with indigo solutions of strengths 33% and 17%, respectively. A part of the solution from the first bottle is thrown away and replaced by an equal volume of the solution from the second bottle. If the strength of the indigo solution in the first bottle has now changed to 21% then the volume, in cc, of the solution left in the second bottle is

**3)Â Answer:Â 200**

**Solution:**

Let Bottle A haveÂ an indigo solution of strength 33%Â whileÂ Bottle B have an indigo solution of strength 17%.

The ratio in which we mix these two solutions to obtain a resultant solution of strength 21% :Â $\frac{A}{B}=\frac{21-17}{33-21}=\frac{4}{12}or\ \frac{1}{3}$

Hence, three parts of the solution from BottleÂ B is mixed with one part of the solution from Bottle A. For this process to happen, we need to displace 600 cc of solution from Bottle A and replace it with 600 cc of solution from Bottle B {since both bottles have 800 cc, three parts of this volume = 600cc}.As a result, 200 cc of the solution remains in Bottle B.

Hence, the correct answer is 200 cc.

**Instructions**

Directions for the following two questions: Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with others.

Option A: Invest in a public sector bank. It promises a return of +0.10%.

Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5%, while a fall will entail a return of â€“ 3%.

Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of â€“ 2.5%, while a fall will entail a return of + 2%.

**Question 4:Â **The maximum guaranteed return to Shabnam is

a)Â 0.25%

b)Â 0.10%

c)Â 0.20%

d)Â 0.15%

e)Â 0.30%

**4)Â AnswerÂ (C)**

**Solution:**

Let a, b and c be the percentages of amountÂ invested in options A, B and C respectively => a + b + c = 100

Return attained if there is a rise in the stock market => 0.001a + 0.05b – 0.025c

Return attained if there is a fall in the stock market => 0.001a –Â 0.03b +Â 0.02c

Maximum guaranteed return is attained when both are equal because it is indifferent to rise and fall in the market.

0.001a + 0.05b – 0.025c =Â 0.001a –Â 0.03b +Â 0.02c

=> 0.08b = 0.045c => 16b = 9c

Let’s put the values for a, b and c that satisfy the above equation.

b = 9, c = 16,Â a = 75 => return = 0.125

b = 18, c = 32, a = 50 => return = 0.15

b = 27, c = 48, a = 25 => return = 0.175

b = 36, c = 64, a = 0 => return = 0.2

Hence, the maximum guaranteed returnÂ is 0.2%

**Question 5:Â **What strategy will maximize the guaranteed return to Shabnam?

a)Â 100% in option A

b)Â 36% in option B and 64% in option C

c)Â 64% in option B and 36% in option C

d)Â 1/3 in each of the three options

e)Â 30% in option A, 32% in option B and 38% in option C

**5)Â AnswerÂ (B)**

**Solution:**

Let a, b and c be the percentages of amountÂ invested in options A, B and C respectively => a + b + c = 100

Return attained if there is a rise in the stock market => 0.001a + 0.05b – 0.025c

Return attained if there is a fall in the stock market => 0.001a –Â 0.03b +Â 0.02c

Maximum guaranteed return is attained when both are equal because it is indifferent to rise and fall in the market.

0.001a + 0.05b – 0.025c =Â 0.001a –Â 0.03b +Â 0.02c

=> 0.08b = 0.045c => 16b = 9c

Let’s put the values for a, b and c that satisfy the above equation.

b = 9, c = 16,Â a = 75 => return = 0.125

b = 18, c = 32, a = 50 => return = 0.15

b = 27, c = 48, a = 25 => return = 0.175

b = 36, c = 64, a = 0 => return = 0.2

Hence, the maximum guaranteed returnÂ is 0.2% and it is attained when 36% is invested in option B and 64% is invested in option C.

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**Question 6:Â **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)Â (+)10

b)Â (-)1

c)Â (+)1

d)Â (-)10

**6)Â AnswerÂ (B)**

**Solution:**

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 = $(600 (\frac{100}{99} – 1)) \div (600(\frac{100}{99})) \times 100 = 1$

**Question 7:Â **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)Â 28.56%

b)Â 35%

c)Â 22.22%

d)Â None of these

**7)Â AnswerÂ (A)**

**Solution:**

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.

**Question 8:Â **Ravi invests 50% of his monthly savings in fixed deposits. Thirty percent of the rest of his savings is invested in stocks and the rest goes into Ravi’s savings bank account. If the total amount deposited by him in the bank (for savings account and fixed deposits) is Rs 59500, then Ravi’s total monthly savings (in Rs) is

**8)Â Answer:Â 70000**

**Solution:**

Let his total savings be 100x.

He invests 50x in fixed deposits. 30% of 50x, which is 15x is invested in stocks and 35x goes to savings bank.

It is given 85x = 59500

x = 700

Hence, 100x = 70000

**Question 9:Â **The income of Amala is 20% more than that of Bimala and 20% less than that of Kamala. 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

a)Â 31

b)Â 29

c)Â 28

d)Â 32

**9)Â AnswerÂ (A)**

**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 new income of Kamala = 150a-150a(4/100) = 150a-6a=144a

If Bimla’s income goes up by 10 percent, her new income will be 100a+100a(10/100)=110a

=> Hence the Kamala income will exceed Bimla income by (144a-110a)*100/110a=31

**Question 10:Â **Meena scores 40% in an examination and after review, even though her score is increased by 50%, she fails 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 for passing the examination is

a)Â 60

b)Â 80

c)Â 70

d)Â 75

**10)Â AnswerÂ (C)**

**Solution:**

Assuming the maximum marks =100a, then Meena got 40a

After increasing her score by 50%, she will get 40a(1+50/100)=60a

Passing score = 60a+35

Post review score after 20% increase = 60a*1.2=72a

=>Hence, 60a+35+7=72a

=>12a=42Â Â =>a=3.5

=> maximum marks = 350 and passing marks = 210+35=245

=> Passing percentage = 245*100/350 = 70