## Percentage Problems for CAT with Solutions

Download important CAT Percentage Questions PDF based on previously asked questions in CAT exam. Practice Percentage problems with solutions for CAT exam.

Download Percentage Problems for CAT with Solutions

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**Question 1: **Let A and B be two solid spheres such that the surface area of B is 300% higher than the surface area of A. The volume of A is found to be k% lower than the volume of B. The value of k must be

[CAT 2003 leaked]

a) 85.5

b) 92.5

c) 90.5

d) 87.5

**Question 2: **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) p = q

b) p < q

c) p > q

d) p = q/2

**Question 3: **A college has raised 75% of the amount it needs for a new building by receiving an average donation of Rs. 600 from the people already solicited. The people already solicited represent 60% of the people the college will ask for donations. If the college is to raise exactly the amount needed for the new building, what should be the average donation from the remaining people to be solicited?

a) Rs. 300

b) Rs. 250

c) Rs. 400

d) 500

**Question 4: **Fresh grapes contain 90% water by weight while dried grapes contain 20% water by weight and the remaining proportion being pulp. What is the weight of dry grapes available from 20 kg of fresh grapes?

a) 2 kg

b) 2.4 kg

c) 2.5 kg

d) None of these

**Question 5: **A student gets an aggregate of 60% marks in five subjects in the ratio 10 : 9 : 8 : 7 : 6. If the passing marks are 50% of the maximum marks and each subject has the same maximum marks, in how many subjects did he pass the examination?

a) 2

b) 3

c) 4

d) 5

**Question 6: **Fresh grapes contain 90% water while dry grapes contain 20% water. What is the weight of dry grapes obtained from 20 kg fresh grapes?

a) 2 kg

b) 2.5 kg

c) 2.4 kg

d) None of these

**Question 7: **One bacterium splits into eight bacteria of the next generation. But due to environmental condition only 50% survives and remaining 50% dies after producing next generation. If the seventh generation number is 4,096 million, what is the number in first generation?

a) 1 million

b) 2 million

c) 4 million

d) 8 million

**Question 8: **A manufacturer has 200 litres of acid solution which has 15% acid content. How many litres of acid solution with 30% acid content may be added so that acid content in the resulting mixture will be more than 20% but less than 25%?

a) More than 100 litres but less than 300 litres

b) More than 120 litres but less than 400 litres

c) More than 100 litres but less than 400 litres

d) More than 120 litres but less than 300 litres

e) None of the above

**Question 9: **Ram prepares solutions of alcohol in water according to customers’ needs. This morning Ram has prepared 27 litres of a 12% alcohol solution and kept it ready in a 27 litre delivery container to be shipped to the customer. Just before delivery, he finds out that the customer had asked for 27 litres of 21% alcohol solution. To prepare what the customer wants, Ram replaces a portion of 12% solution by 39% solution. How many litres of 12% solution are replaced?

a) 5

b) 9

c) 10

d) 12

e) 15

**Question 10: **M/s. Devi Radiograms, a shop which sells electronic gadgets, marks its merchandise 35% above the purchase price. Until four months ago, purchase price of one Philips DVD player was Rs. 3,000. During the last four months M/s. Devi Radiograms has received four monthly consignments of Philips DVD player at the purchase price of Rs. 2,750, Rs. 2,500, Rs. 2,400, and Rs. 2250. The average rate of decrease in the purchase price of DVD player during these four months is:

a) 7.5%

b) 8.20%

c) 6.9%

d) 7%

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**Answers & Solutions:**

**1) Answer (D)**

Surface area of sphere A (of radius a) is $4\pi*a^2$

Surface area of sphere B (of radius b) is $4\pi*b^2$

=> $4\pi*a^2$/$4\pi*b^2$ = 1/4 => a:b = 1:2

Their volumes would be in the ratio 1:8

Therefore, k = 7/8 * 100% = 87.5%

**2) Answer (C)**

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.

**3) Answer (A)**

Let there be total 100 people whom the college will ask for donation. Out of these 60 people have already given average donation of 600 Rs. Thus total amount generated by 60 people is 36000. This is 75% of total amount required . so the amount remaining is 12000 which should be generated from remaining 40 people. So average amount needed is 12000/40 = 300

**4) Answer (C)**

In 20kg fresh grapes, the weight of water is 18kg and the weight of pulp is 2kg.

The concept that we apply in this question is that the weight of pulp will remain the same in both dry and fresh grapes. For example, 100 kg of fresh grapes will contain 90 kg of water and 10 kg pulp. If this grape is dried, the water content will change but pulp content will remain the same.

So, for 2kg of pulp,

80% of the weight of dry grapes = 2

20% water weight=2/4=0.5

Weight of dry grapes =water content+pulp= 2.5 kg

**5) Answer (C)**

Let’s say he scored marks as $10x,9x,8x,7x,6x$ or total of $40x$ which is 60% of total maximum marks(T).

$\frac{T \times 60}{100}=40x$

So T (total maximum marks)=$\frac{400x}{6}$

Or Individual max. marks = $\frac{T}{5}=\frac{80x}{6}$

Passing marks =50% of individual max. marks =$\frac{40x}{6}=6.66x$

Hence he scored more than passing marks in four subjects as $10x,9x,8x$ and $7x$

and failed in one subject as scoring $6x$ marks which is less than passing marks of $6.66x$

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**6) Answer (B)**

Let the total weight of fresh grapes be 100 gm.

=> Fresh grapes have 90 gm of water and 10 gm of fruit.

When these grapes are dried, the amount of fruit does not change.

=> 10 grams will become 80% of the content in dry grapes

=> Weight of dry grapes = $\frac{10}{0.8}$ = 12.5 gm

So, the weight of fresh grapes reduces to 1/8th of its original weight.

=> 20 kg of fresh grapes give 2.5 kg of dry grapes.

**7) Answer (A)**

let’s say x is the initial number of bacterias :

So in 2nd generation no. of bacterias = \frac{8x}{2} = 4x

In 3rd generation, it will be = 16x

4th gen. = 64x

5th gen. = 256x

6th gen. = 1024x

7th gen. = 4096x

Hence x = 1 million

**8) Answer (C)**

Let the volume of the solution with 30 % acid content lie between $v_1$ and $v_2$, where we get a 20% acid solution for $v_1$

For $v_2$, we get a 25 % acid solution as the resultant mixture.

=> $15 \% (200) + 30 \% (v_1) = 20 \% (200 + v_1)$

=> $30 + 0.3 v_1 = 40 + 0.2 v_1$

=> $0.1 v_1 = 10$ => $v_1 = 10 \times 10 = 100$ litres

Similarly, $15 \% (200) + 30 \% (v_2) = 25 \% (200 + v_2)$

=> $30 + 0.3 v_2 = 50 + 0.25 v_2$

=> $0.05 v_2 = 20$ => $v_2 = 20 \times 20 = 400$ litres

$\therefore$ For the acid content in the resultant mixture to lie between 20 % and 25 %, the volume of the 30 % concentration acid solution must lie between 100 litres and 400 litres.

**9) Answer (B)**

Let Ram replaces $x$ litres of 12 % sol. with 39 % solution

Now, quality of 12 % solution in 27 litre = $\frac{12}{100} \times 27$

=> After replacing we have volume of 12 % solution

= $(\frac{12}{100} \times 27) – (\frac{12 x}{100}) + (\frac{39 x}{100})$

= $\frac{324 + 27 x}{100}$

This is equal to 27 litre of 21 % solution.

=> $\frac{324 + 27 x}{100} = \frac{21}{100} \times 27$

=> $27x = 567 – 324 = 243$

=> $x = \frac{243}{27} = 9$

**10) Answer (C)**

decrease in purchase price for first month was $\frac{3000-2750}{3000}$ = 0.083

decrease in purchase price for second month was $\frac{2750-2500}{2750}$ = 0.0909

decrease in purchase price for the third month was $\frac{2500-2400}{2500}$ = 0.04

decrease in purchase price for the fourth month was $\frac{2400-2250}{2400}$ = 0.0625

Average decrease = $\frac{0.083+0.0909+0.04+0.0625}{4}$ = 0.069 i.e 6.9%

Therefore our answer is option’C’

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