1EasyTITA
A sum of money is divided among P, Q, and R in the ratio 2:3:4. If P gets 4000, what is the total sum?
Ratio, Proportion and Variation Questions for CAT
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132 easy235 medium142 hard
Ratio and Proportion is the connective tissue of CAT arithmetic, it appears inside profit and loss, time and work, mixtures and time-speed-distance far more often than it appears as a standalone question. Being fluent here makes every other arithmetic topic faster, because ratio methods usually replace an equation with a single line of scaling. That is why it is worth practising in volume even though it looks elementary.
20 free Ratio, Proportion and Variation questions
2EasyMCQ
If , what is the ratio of to ?
- A
- B
- C
- D
3EasyTITA
A, B, C invest in a business in the ratio 2:3:5. Total profit is 10000. Find C's share.
4EasyMCQ
Ajit goes to the market with a certain amount of money. With this money, he can purchase either 100 apples or 80 mangoes. He needs to set aside 20% of the money for taxi fare. If he buys 40 apples, how many mangoes can he afford?
- A
38 mangoes
- B
24 mangoes
- C
40 mangoes
- D
32 mangoes
5EasyTITA
A shopkeeper stocks oranges, pears, and grapes, with at least one of each. At the start of the day, oranges make up 30% of the total stock. During the day, he sells one-third of the oranges, 84 pears, and 25% of the grapes. By the end of the day, exactly 45% of the fruits have been sold. What is the smallest possible total number of fruits at the start of the day?
6EasyMCQ
The difference between two positive numbers is 11 and the ratio between them is . Find the product of the two numbers.
- A
242
- B
225
- C
272
- D
152
7MediumMCQ
Two farmers were cultivating wheat on their respective agricultural land in a village. Farmer A had an average production of 20 bushels from a hectare. Farmer B, who had 15 hectares of more land dedicated to wheat cultivation, had and output of 30 bushels of wheat from a hectare. If farmer B harvested 530 bushels of wheat more than farmer A, how many bushels of wheat did farmer A cultivate?
- A
50
- B
80
- C
160
- D
200
8MediumMCQ
A fruit seller has oranges, apples, and guavas in the ratio of 2:5:8. The number of apples exceeds the number of oranges by an amount that is a multiple of both 6 and 8. What is the smallest total number of fruits in his shop?
- A
240
- B
360
- C
120
- D
90
9MediumMCQ
A, B, and C each have some coins. Seven times the number of coins A has equals five times the number of coins B has, while six times the number of coins B has equals eleven times the number of coins C has. What is the smallest total number of coins that A, B, and C have combined?
- A
110
- B
174
- C
154
- D
165
10MediumMCQCAT 2025
A cord is 72 cm long. It is cut into three pieces. The longest piece is twice the length of the shortest piece, and the middle piece is 8 cm longer than the shortest piece. Find the length of the shortest piece.
- A
16
- B
18
- C
20
- D
24
11MediumMCQ
A factory produces a certain number of shirts everyday. 20% of the shirts produced are defective. The non-defective shirts are sold at domestic and international markets. 30% of the shirts sold in the domestic markets are sold in combo offers and 20% of the shirts sold in the international market are sold in combo offers. If the total number of shirts sold in combo offers is twice the number of shirts sold in combo offers in international markets, then the ratio of the number of shirts sold in the domestic market to the number of shirts sold in the international market is
- A
2:3
- B
3:2
- C
2:1
- D
3:1
12MediumTITA
At a ticket counter, the ratio of the number of people ahead of Sohan to the number of people behind him is 7 : 9. If the total number of people in the queue is less than 600, then what is the maximum possible number of people standing ahead of Sohan?
13MediumMCQ
An outgoing batch wants to gift a PA system worth Rs. 4200. If teachers offer to pay 50% more than the students, and an external benefactor gives three times the teachers’ contribution, how much should the teachers donate?
- A
600
- B
840
- C
900
- D
1200
14MediumMCQ
Five years ago, the ratio of the ages of Hari and his father was 2 : 5. Five years hence, the ratio of the ages of Hari and his mother will be 3 : 5. What is the sum of the present ages of all three, if the ratio of the present ages of Hari's mother and Hari's father is 9 : 11?
- A
125 years
- B
100 years
- C
120 years
- D
140 years
15HardMCQ
Akshay, Bala, and Chinmay distribute money in turn: Akshay gives an amount that causes Bala and Chinmay's money to quadruple, Bala gives an amount that causes Akshay and Chinmay's money to triple, and Chinmay gives an amount that causes Akshay and Bala's money to double. In the end, Akshay is short by Rs.105, Chinmay is short by Rs.2, and Bala gains Rs.107. What could their initial ratio have been?
- A
16:4:1
- B
249:61:14
- C
41:6:2
- D
50:24:7
16HardMCQ
A coin box contains 50 paise, 1 rupee and 2 rupee coins. The total number of coins is 400 and the total value is Rs 460. If the numbers of 50 paise and 1 rupee coins are interchanged, the value increases by Rs 20. Find the number of 2 rupee coins.
- A
100
- B
136
- C
146
- D
160
17HardMCQ
X, Y and Z invest in a partnership where X invests 60% of the total. If the overall profit rate decreases from 20% to 16%, X's profit share falls short by ₹720. Also, Z’s profit share rises by ₹100 when the overall profit rate goes up from 16% to 18%. Find Y’s investment amount.
- A
7400
- B
7000
- C
7800
- D
8000
18HardMCQ
An alloy of gold and silver is taken in the ratio of , and another alloy of the same metals is taken in the ratio of . How many parts of the two alloys must be taken to obtain a new alloy consisting of gold and silver that are in the ratio ?
- A
3 and 5
- B
2 and 9
- C
2 and 5
- D
1 and 5
19HardMCQ
The weight of three heaps of gold are in the ratio . By what fractions of themselves must the first two be increased so that the ratio of the weights may be changed to ?
- A
- B
- C
- D
20HardMCQ
In a bookstore, the shelves are arranged in an m×n grid. After removing 24 books, each row contains 7 fiction books and each column contains 9 non-fiction books. What is the minimum possible value of mn?
- A
380
- B
432
- C
768
- D
940
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Ratio, Proportion and Variation for CAT, answered
What CAT asks in Ratio, Proportion and Variation, the mistakes that cost the most marks, and how to practise it.
Simple and compound ratios, dividing quantities in a given ratio, direct and inverse variation, joint variation, and componendo-dividendo style manipulations. It also underpins partnership and mixture questions, which are often classified separately.
Working in ratio units rather than absolute values usually removes the need to find the actual quantities at all. Many questions that look like they need two equations resolve in one line once the ratio is fixed and scaled at the end.
A ratio compares two quantities; a proportion states that two ratios are equal. The distinction matters in practice because proportion questions let you cross-multiply and ratio questions do not, which is a common source of invalid steps.
Every question here has been checked against a worked solution before being published, and anything without a complete solution is not shown at all. The bank mixes questions written for CAT-level practice with questions from actual CAT papers; the previous-year questions are collected separately under CAT PYQs. The solutions themselves open in practice mode once you sign up, which is free.