Solved Examples: Percentages | General Aptitude for GATE - Mechanical Engineering PDF Download

Easy Level

The questions are targeted to improve your knowledge on basic concepts, though easy questions are rare in CAT. These are extremely important for conceptual understanding at the foundation level. Try this question by yourself:

Let's start with the practice questions
Example 1: If all the sides of a cuboid are increased by 20%, then by what percentage does its volume increase?

(a) 20%

(b) 44%

(c) 60%

(d) 72.8% 

Ans: (d)

Solution: Let initially the sides be x, y and z.
► Initial volume = xyz
► After the change sides will be 1.2x, 1.2y and 1.2z.
► New volume = 1.728(xyz)
∴ Increase in volume is 72.8%.

Example 2: In an election between two candidates, the candidate who gets 30% of the votes polled is defeated by 15,000 votes. The number of votes polled in favour of the winning candidate is
(a) 11,250
(b) 15,000
(c) 26,250
(d) 37,500

Ans: (c)

Solution: 

The correct option is C. 26250 

Percentage of votes obtained by defeated party = 30 %

 ∴ Percentage of votes obtained by winning party= 100 % − 30 % = 70 % 

Difference in percentage 70 % − 30 % = 40 % 

Let there be total of x votes. 

Therefore, according to the question, ⇒ 40 % × x = 15000 ⇒ x = 15000 × 100 40 ⇒ x = 37500 

Thus, no. of votes pulled by winning party 70 % × 37500 = 26250

Example 3: In an election between 2 candidates, Chaman gets 80% of the total valid votes. If the total votes were 12000, what is the number of valid votes that the other candidate Dhande gets if 15% of the total votes were declared invalid?

(a) 1645

(b) 1545

(c) 1675

(d) 2040

Ans: (d)

Solution: 

To find the number of valid votes that the other candidate Dhande gets, we need to first calculate the total valid votes.

Given that the total votes were 12,000 and 15% of the total votes were declared invalid, we can calculate the total valid votes as follows:

Total valid votes = Total votes - Invalid votes

Total valid votes = 12,000 - (15/100) * 12,000

Total valid votes = 12,000 - 1,800

Total valid votes = 10,200

Now, since Chaman gets 80% of the total valid votes, we can calculate the number of valid votes that Dhande gets as follows:

Number of valid votes for Dhande = Total valid votes - Votes for Chaman

Number of valid votes for Dhande = 10,200 - (80/100) * 10,200

Number of valid votes for Dhande = 10,200 - 8,160

Number of valid votes for Dhande = 2,040

Therefore, the number of valid votes that the other candidate Dhande gets is 2,040.

Answer: (d) 2040

Medium Level

Almost 70% of questions in CAT are of Medium based questions. Though the conceptually they seem easier, the trick is to solve the calculations faster & we curated problems for you to help you do problems easier.

Example 1: A sum of money compounded annually becomes Rs. 625 in 2 years and Rs. 675 in 3 years. The rate of interest per annum is 

(a) 7% 

(b) 10%

(c) 5% 

(d) 8% 

Ans: (d)

Solution: For a difference of 1 year, C.I. can be computed as S.I.
► Hence, from the 2nd year to the 3rd year, interest earned = (675 – 625) = Rs. 50 on Rs. 625.
► Hence, the rate of interest = 50 /625 × 100 = 8% per annum.

Example 2: I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was 50% more than what I had paid. What percentage of the total amount spent by me was spent on pens?

(a) 37.5%

(b) 56.5%

(c) 50% 

(d) 62.5%

Ans: (d)

Solution: Let us look at the two equations:
► Let (5 pens + 7 pencils + 4 erasers) cost Rs. x, and (6 pens + 14 pencils + 8 erasers) will cost Rs. 1.5x
► In the second case, had Rajan decided to buy 10 pens instead of 6, it would have cost him Rs. 2x
∴ (10 pens + 14 pencils + 8 erasers) = Rs. 2x
► Now, subtracting the second equation from the third, we get 4 pens cost Rs. 0.5x. So, 5 pens will cost Rs. 0.625 x. This is the amount that I have spent on pens.
► Hence, fraction of the total amount paid = 0.625 = 62.5%

Example 3: Rehman buys a few apples at 15 for a rupee and the same number of apples at 20 for a rupee. He mixes the two lots and sells them at 35 for 2 rupees. What is his gain or loss percentage? 

(a) 3.62% loss 

(b) 2.04% profit 

(c) No profit, no loss

(d) 2.04% loss 

Ans: (d)

Solution: Suppose Rehman buys ( LCM of 15, 20 and 35)  420 apples.
► Total cost of apples bought at 15 for a rupees  = 420/15 = Rs. 28
► Total Cost of apples bought at 20 for a rupees = 420/20 = Rs. 21
∴ Total C.P = Rs. (28+21) = Rs. 49
► S.P for (420+420) 840 apples = Rs. (840 x 2) / 35 = Rs. 48
∴ Loss % = (49 - 48)/49 x 100 = 2.04%.

Hard Level

Around 25% of these type questions come in CAT - If your target is above 95%ile, we recommend you to solve these questions as well.

Example 1: There are three galleries in a coal mine. On the first day, two galleries are operative and after some time, the third gallery is made operative. With this, the output of the mine became half as large again. What is the capacity of the second gallery as a percentage of the first, if it is given that a four-month output of the first and the third galleries were the same as the annual output of the second gallery? 

(a) 70% 

(b) 64% 

(c) 60% 

(d) 65%

Ans: (c)

Solution: The third gallery making the capacity ‘half as large again’ means an increase of 50%. 

► Further, it is given that: 4(first + third) = 12 (second) In order to get to the correct answer, try to fit in the options into this situation. (Note here that the question is asking you to find the capacity of the second gallery as a percentage of the first.)
► If we assume option (a) as correct – 70% the following solution follows: If the second is 70, then first is 100 and first + second is 170. Then third will be 85 (50% of first + second). Then the equation: 4 * (100 + 85) should be equal to 12*70 But this is not true.
► Through trial and error, you can see that the third option fits correctly. 4 * (100 + 80) = 12 * 60.
Hence, it is the correct answer.

Example 2: A shopkeeper announces a discount scheme as follows: for every purchase of ₹ 3000 to ₹ 6000, the customer gets a 15% discount or a ticket that entitles him to get a 7% discount on a further purchase of goods costing more than ₹ 6000. The customer, however, would have the option of reselling his right to the shopkeeper at 4% of his initial purchase value (as per the right refers to the 7% discount ticket). In an enthusiastic response to the scheme, 10 people purchase goods worth ₹ 4000 each. Find the maximum. Possible revenue for the shopkeeper.

(a) ₹ 38,400 

(b) ₹ 38,000 

(c) ₹ 39,400 

(d) ₹ 39,000

Ans: (a)

Solution: The shopkeeper would get the maximum revenue when everybody opts for a 4% resale of the right.
► In such a case, the shopkeeper's revenue from each customer would be 96% of 4000 = 4000 – 160 = 3840.
► Hence, the total revenue is 38400.