Introduction
This is a practice document for your conceptual strengthening. The main idea of this document is to practice the questions before you go and attempt your nationwide tests @EduRev so that you will be more relating to questions asked in that exam & be more confident about your answers.
All The Best!
Easy Level
At this level, questions are targeted to improve your knowledge of basic concepts, though easy questions are rare in CAT. These are extremely important for conceptual understanding at the foundation level. Try this past year question by yourself first.
Question for Practice Questions: Ratio & Proportion
Try yourself:PYQ(CAT 2017): 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?
Explanation
Arun’s age will be = 4x. The difference of these age in 6x When Arun’s age is 50% of Barun’s age, this difference also would be 50%
i.e. Barun’s age at that stage would be 12x. It would be increase by 20%
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Let's start with the practice questions
Example 1: If three numbers are in the ratio of 1 : 3 : 5 and half the sum is 9, then the ratio of cubes of the numbers is:
(a) 6 : 12 : 13
(b) 1 : 3 : 25
(c) 1 : 27 : 125
(d) 3 : 5 : 7
Ans. (c)
Solution: 1 : 3 : 5
► So x, 3x and 5x add up to 18.
► So the numbers are 2, 6 and 10.
► Ratio of cubes = 8 : 216 : 1000 = 1: 27: 125.
Example 2: Three quantities A, B, C are such that AB = KC, where k is a constant. When A is kept constant, B varies directly as C; when B is kept constant, A varies directly C and when C is kept constant, A varies inversely as B. Initially, A was at 5 and A : B : C was 1 : 3 : 5. Find the value of A when B equals 9 at constant C.
(a) 8
(b) 8.33
(c) 9
(d) 9.5
Ans. (b)
Solution:
► Initial values are 5, 15 and 25.
► Thus we have 5 * 15 = K * 25.
► Hence, K = 3.
► Thus, the equation is AB = 3C.
► For the problem, keep C constant at 25.
► Then, A * 9 = 3 * 25. i.e., A = 75/9 = 8.33
Example 3: A began a business with Rs. 4,500 and was joined afterwards by B with Rs. 5,400. If the profits at the end of the year were divided in the ratio 2 : 1, then B joined the business after:
(a) 5 months
(b) 4 months
(c) 6 months
(d) 7 months
Ans. (d)
Solution:
► The ratio of profit-sharing = 4500 × 12: 5400 × n where n is the period for which B invested.
► Ratio = 4500 × 12 : 5400 × n = 10 : n
► Now, this ratio is equal to 2 : 1
∴ 10 : n = 2 : 1 ⇒ n = 5 months
► Thus, B joined A after 12 – 5 = 7 months
Question for Practice Questions: Ratio & Proportion
Try yourself:X varies jointly as Y and Z; and X = 6 when Y = 3, Z = 2; find X when Y = 5, Z = 7.
Explanation
X = K *Y * Z It is known that when X = 6, Y = 3 and Z = 2. Thus we get 6 = 6K ;K = 1. Thus, our relationship between X, Y and Z becomes X = Y * Z.
Thus, when Y = 5 and Z = 7 we get X = 35
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Question for Practice Questions: Ratio & Proportion
Try yourself:3650 is divided among 4 engineers, 3 MBAs and 5 CAs such that 3 CAs get as much as 2 MBAs and 3 Engineers as much as 2 CAs. Find the share of an MBA.
Explanation
4E + 3M + 5C = 3650 Also, 3C = 2M, that is, M = 1.5 C and 3E = 2C that is, E = 0.66C Thus, 4 *0.66C + 3 * 1.5 C + 5C = 3650 C = 3650/12.166
That is, C = 300 Hence, M = 1.5 C = 450
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Question for Practice Questions: Ratio & Proportion
Try yourself:Divide Rs rs.5000 among A, B, C and D so that A and B together get 3/7thof what C and D get together, C gets 1.5 times of what B gets and D gets 4/3 times as much as C. Now the value of what B gets is
Explanation
Check the options, B = 1000 and C = 1.5 * 1000 = 1500, D = 4/ 3 * 1500 = 2000 A = 5000 – 1000 – 1500 – 2000 = 500. Now A + B = 500 + 1000 = 1500, C + D = 1500 + 2000 = 3500. As 1500 = 3/ 7 *3500. So this option is correct
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Question for Practice Questions: Ratio & Proportion
Try yourself:A bag contains Rs. 600 in the form of one rupee, 50 paise and 25 paise coins in the ratio of 3 : 4 : 12. Find the total value (in Rs.) of the 25 paise coins present in the bag.
Explanation
Let the number of one rupee coins, 50 paise coins and 25 paise coins be 3x, 4x and 12x respectively. Value of one rupee coins = 3x, 50 paise coins = 4x /2 and 25 paise coins = 12x/ 4 Thus, 3x + 2x + 3x = 600 ⇒ x = 75 Therefore, value of 25 paise coins = 12 ×75/ 4 =Rs. 225.
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Question for Practice Questions: Ratio & Proportion
Try yourself:Divide Rs.1400 into three parts in such a way that half of the first part, one-fourth of the second part and one-eighth of the third part are equal.
Explanation
Solve this question using options. 1/2 of the first part should equal 1/4th of the second part and 1/8th of the third part. Only, option (b) satisfies these conditions thus this option is correct.
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Question for Practice Questions: Ratio & Proportion
Try yourself:The students in three batches at EduRev are in the ratio 2 : 3 : 5. If 20 students are increased in each batch, the ratio changes to 4 : 5 : 7. The total number of students in the three batches before the increases were
Explanation
2x + 20 : 3x + 20 : 5x + 20 = 4 : 5 : 7 i.e, x = 10 and initially the number of students would be 20, 30 and 50 so a total of 100.
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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: Monthly incomes of X and Y are in the ratio 1 : 3 and their expenses are in the ratio 19 : 40. X saves Rs. 18,860 less than that Y and in total they save Rs. 36,020. The income of X and Y respectively are:
(a) Rs. 10,480 and Rs. 31440
(b) Rs. 9,000 and Rs. 27,000
(c) Rs. 14,200 and Rs. 42,600
(d) Rs. 18,000 and Rs. 31,440
Ans. (a)
Solution: Let the income of X be Rs. p and income of Y be Rs. 3p
► Let expenses of X be Rs. 19q and expenses of Y be Rs. 40q
► Hence, savings of X = Rs. (p – 19q) and savings of Y = Rs. (3p – 40q)
► Total savings = (4p – 59q) = 36020
► Difference of savings = (2p – 21q) = 18860
► Solving the above equations, we get p = 10480
► Thus, the income of X and Y is Rs. 10,480 and Rs. 31, 440, respectively.
Example 2: A student scored marks in the ratio 5 : 4 : 6 : 8 : 7 in five subjects having equal maximum marks. In all, he scored 50% of the maximum marks in all the five subjects taken together. In how many subjects did he score more than 55% of the maximum marks?
(a) 1
(b) 2
(c) 3
(d) 4
Ans. (b)
Solution: Let his marks be 5x, 4x, 6x, 8x, and 7x respectively.
► Aggregate marks obtained = 30x = 50% of aggregate maximum marks.
► Thus, aggregate maximum marks = 60x
► Maximum marks per subject = 12 x 55% of maximum marks per subject = 6.6x
► Hence in two subjects, marks are more than 6.6x.
Example 3: A person buys some apples and mangoes from the market. The cost price of a mango is twice that of an apple and the selling price of a mango is thrice that of an apple. By selling an apple at twice its cost price, he makes 150% profit on the whole. Find the ratio of the number of mangoes to that of apples that he bought from the market.
(a) 3 : 5
(b) 3 : 4
(c) 1 : 2
(d) 2 : 3
Ans. (c)
Solution: Suppose the person buys apples and M mangoes and the cost price of an apple is Rs. x.
► Therefore, the cost price of the mango will be 2x.
► Total cost price = Ax + 2Mx.
► Now the selling price of an apple is 2x.
∴ SP of a mango will be 6x.
► Total SP = 2Ax + 6Mx.
► Now we have 2Ax + 6Mx = 5 2 (Ax + 2Mx) or M/A=½.
Question for Practice Questions: Ratio & Proportion
Try yourself:The ratio of the first class fare and second class fare is 3 : 1 and that of the number of passengers traveling by the first class and by the second class is 1 : 27. If Rs. 2,700 is collected as fare, then the amount collected from the first class passengers is
Explanation
Ratio of amounts collected from first and second classes = (3 × 1) : (1 × 27) = 1 : 9 So, amount collected from first class passenger is = 1 /10 Rs. × 2700 = Rs. 270.
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Question for Practice Questions: Ratio & Proportion
Try yourself:The ratios of the incomes and the expenditures of Aishwarya, Babita and Charu are 7 : 9 : 12 and 8 : 9 : 15 respectively. If Aishwarya saves one-fourth of her income, then the ratio of their savings is
Explanation
Let the incomes (in Rs.) of Aishwaraya, Babita and charu be 7x, 9x and 12x and their expenditures (in Rs.) be 8y, 9y and 15y respectively. Then,
So their respective incomes ( in Rs. ) are 32y/3, 96y/7 and 128y/7 and respective savings ( in Rs. ) will be 8y/3, 33y/7 and 23y/7.
Hence , the required ratio is 56 : 99 : 69
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Question for Practice Questions: Ratio & Proportion
Try yourself:Total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. The average expense per boarder is Rs. 700 when there are 25 boarders and Rs. 600 when there are 50 boarders. What is the average expense per boarder when there are 100 boarders? (CAT 1999)
Explanation
Let x be the fixed cost and y the variable cost.
Then, 17500 = x + 25y … (i) 30000 = x + 50y … (ii)
Solving the equation (i) and (ii),
we get x = 5000, y = 500
Now if the average expense of 100 boarders be ‘A’.
Then 100 × A = 5000 + 500 × 100 ⇒ A = Rs. 550.
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Question for Practice Questions: Ratio & Proportion
Try yourself:Sahil employs 200 men to build a bund. They finish 5/6 of the work in 10 weeks. Because of some natural calamity not only does the work remain suspended for 4 weeks but also half of the work already done is washed away. After the calamity, when the work is resumed, only 140 men turn up. The total time in which the contractor is able to complete the work assuming that there are no further disruptions in the schedule
Explanation
In 2000 man weeks before the calamity, 5/6th of the work is completed. Hence, 2400 men weeks will be the total amount of work. However, due to the calamity half the work gets washed off → This means that 1000 man weeks worth of work must have got washed off. This leaves 1400 men weeks of work to be completed by the 140 men. They will take 10 more weeks and hence the total time required is 24 weeks
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Question for Practice Questions: Ratio & Proportion
Try yourself:A bag contains 25 paise, 50 paise and 1 Rupee coins. There are 220 coins in all and the total amount in the bag is Rs160. If there are thrice as many 1 Rupee coins as there are 25 paise coins, then what is the number of 50 paise coins?
Explanation
Let the number of coins of Rs 1, 50 p, 25 p be A, B and C respectively.
A + B + C = 220 ---(1)
A = 3C ---(2)
A + 0.5B + 0.25C = 160 ---(3)
We have a situation with 3 equations and 3 unknowns. We can solve for A (no. of 1 rupee coins), B (no. of 50 paise coins) and C (no. of 25 paise coins) However, a much smarter approach would be to go through the options.
By this we get B as 60 coins, C as 40 coins & A to be 120.
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Question for Practice Questions: Ratio & Proportion
Try yourself:A mother divided an amount of Rs 61,000 between her two daughters aged 18 years and 16 years respectively and deposited their shares in a bond. If the interest rate is 20% compounded annually and if each received the same amount as the other when she attained the age of 20 years, their shares are
Explanation
This is a simple question if you can catch hold of the logic of the question, i.e., the younger daughter’s share must be such after adding a CI of 20% for two years, she should get the same value as her elder sister. None of the options meets this requirement.
Hence, None of these is correct
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Question for Practice Questions: Ratio & Proportion
Try yourself:40 men could have finished the whole project in 28 days but due to the inclusion of a few more men, work got done in 3/4 of the time. Find out how many more men were included (in whole numbers).
Explanation
Since, the work gets done in 25% less time there must have been an addition of 33.33% men. This would mean 13.33 men extra SO which would mean 14 extra men (in whole numbers
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Hard Level
Around 25% of these types of questions come in CAT - If your target is above 95%ile, we recommend you solve these questions.
Example 1: From a full barrel containing 729 litres of honey, we pour off ‘a’ litre and add water to fill up the barrel. After stirring the solution thoroughly, we pour off ‘a’ litre of the solution and again add water to fill up the barrel. After the procedure is repeated 6 times, the solution in the barrel contains 64 litres of honey. Find a.
(a) 243 litres
(b) 81 litres
(c) 2.7 litres
(d) 3 litres
Ans. (a)
Solution:
► Check each of the options as follows: Suppose you are checking option b which gives the value of as 81 litres. Then, it is clear that when you are pouring out 81 litres, you are leaving 8/9 of the honey in the barrel.
► Thus, the amount of honey contained after 6 such operations will be given by
= 729 X (8/9)6. If this answer has to be correct, this value must be equal to 64 (which it clearly is not since the value will be in the form of a fraction.)
► Hence, this is not the correct option. You can similarly rule out the other options.
Example 2: There are two alloys of gold, silver and platinum. The first alloy is known to contain 40 per cent of platinum and the second alloy 26 per cent of silver. The percentage of gold is the same in both alloys. Having alloyed 150 kg of the first alloy and 250 kg of the second, we get a new alloy that contains 30 per cent of gold. How many kilograms of platinum is there in the new alloy?
(a) 170 kg
(b) 175 kg
(c) 160 kg
(d) 165 kg
Ans. (a)
Solution: Since the percentage of gold in both alloys is the same, any mixture of the two will contain the same percentage concentration of gold.
Hence, we get
Question for Practice Questions: Ratio & Proportion
Try yourself:In two alloys, the ratios of nickel to tin are 5 : 2 and 3 : 4 (by weight). How many kilogram of the first alloy and of the second alloy should be alloyed together to obtain 28 kg of a new alloy with equal contents of nickel and tin?
Explanation
It is clear that if 7 kg of the first is mixed with 21 kg of the second you will get 5 + 9 = 14 kg of nickel and 14 kg of tin. You do not need to check the other options since they will go into fractions.
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Question for Practice Questions: Ratio & Proportion
Try yourself:Total expenses of running the hostel at Harvard Business School are partly fixed and partly varying linearly with the number of boarders. The average expense per boarder is $70 when there are 25 boarders and $60 when there are 50 boarders. What is the average expense per boarder when there are 100 boarders?
Explanation
When there are 25 boarders, the total expenses are $1750. When there are 50 boarders, the total expenses are $ 3000. The change in expense due to the coming in of 25 boarders is $ 1250. Hence, expense per boarder is equal to $50. This also means that when there are 25 boarders, the variable cost would be 25 X 50 = $1250.
Hence, $500 must be the fixed expenses.
So for 100 boarders, the total cost would be: $ 500 (fixed) + $ 5000 = $5500
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Question for Practice Questions: Ratio & Proportion
Try yourself:Gunpowder can be prepared by saltpetre and nitrous oxide. Price of saltpetre is thrice the price of nitrous oxide. Notorious gangster Kallu Bhai sells the gunpowder at Rs 2160 per 10 g, thereby making a profit of 20%. If the ratio of saltpetre and nitrous oxide in the mixture be 2 : 3, find the cost price of saltpetre.
Explanation
The cost of making one gram of gun powder would be Rs 180. This will contain 0.4 gm of saltpetre and 0.6 gm of nitrous oxide. Check through options. At the rate of saltpetre of 300/gm, the nitrous oxide will cost Rs100/gm. The total cost of 0.4 grams of saltpetre will be 120 and 0.6 grams of nitrous oxide will be Rs 60 giving the total cost as 180.
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