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**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:

Try yourself:The price per unit of an article decreases by 4%, and the consumption (in units) decreases by 8%. The expenditure would decrease by

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**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:** Let the total number of votes be x.

Then, 30% of x + 15000 = 70% of x

⇒ 15000 = 0.4x

⇒ x = 37500

The required number = 70% of 37500 = 70 37500 100 = 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:** Total votes = 12000.

► Valid votes = 85% of 12000 = 10200.

► Chaman gets 80% of 10200 votes = 8160 votes

► Dhande would get 10200 – 8160 = 2040 Votes.

*Answer can only contain numeric values

Try yourself:**A batsman scored 100 runs which included 4 boundaries and 6 sixes. What percent of his total score did he make by running between the wickets?**

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Try yourself:In an examination, Madan obtained 20% more than Sahir but 40% less than Ravi. If the marks obtained by Sahir is 80, find the percentage marks obtained by Ravi if the full marks is 200.

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Try yourself:A man borrows Rs 6000 at 5% interest, on reducing balance, at the start of the year. If he repays Rs 1200 at the end of each year, find the amount of loan outstanding, in Rs. at the beginning of the third year. (XAT 2012)

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*Answer can only contain numeric values

Try yourself:A man sells an article at a profit of 20%. If he had bought it at 20% less and sold it for Rs. 5 less, he would have gained 25%. Find the cost price (in Rs.) of the article.

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*Answer can only contain numeric values

Try yourself:A and B are two friends, each having at least a rupee. If A gives B a sum of Rs. 20, then A has 40% of the amount with B. If B gives A, a sum of Rs. 40, then B will have 40% of the amount with A. What is the amount (in Rs.) with A initially?

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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: ****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%.

Try yourself:After how many years (approximately) would the amount payable on a loan be twice the principal, if principal is lent at 20% CI, compounded half yearly?

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Try yourself:Sudhir, a very clever businessman, started off a business with very little capital. In the first year, he earned a profit of 50% and donated 50% of the total capital (initial capital + profit) to a charitable organisation. The same course was followed in the 2nd and 3rd years also. If at the end of three years, he is left with ₹ 33,750, then find the amount donated by him at the end of the 2nd year.

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Try yourself:In the university examination last year, Samanyu scored 65% in English and 82% in History. What is the minimum percent he should score in Sociology, which is out of 50 marks (if English and History were for 100 marks each), if he aims at getting 78% overall?

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Try yourself:Malti has M with her and her friend Chinki has C with her. Malti spends 12% of her money and Chinki also spends the same amount as Malti did. What percentage of her money did Chinki spend?

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Try yourself:Aman’s salary is first increased by 25% and then decreased by 20%. The result is the same as Baman’s salary increased by 20% and then reduced by 25%. Find the ratio of Baman’s initial salary to that of Aman’s initial salary.

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Try yourself:Alok and Bimal have, between them, ₹ 12000. Alok spends 12% of his money while Bimal spends 20% of his money. They are then left with a sum that constitutes 85% of the whole sum. Find what amount is left with Alok.

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*Answer can only contain numeric values

Try yourself:At IIM Bangalore, 60% of the students are boys and the rest are girls. Further 15% of the boys and 7.5% of the girls are getting a fee waiver. If the number of those getting a fee waiver is 90, find the total number of students getting 50% concession if it is given that 50% of those not getting a fee waiver are eligible to get half fee concession?

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**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.

Try yourself:The price of raw materials has gone up by 15%, labour cost has also increased from 25% of the cost of raw material to 30% of the cost of raw material. By how much percentage should there be a reduction in the usage of raw materials so as to keep the cost same?

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Try yourself: A clock is set right at 12 noon on Monday. It loses 1/2% on the correct time in the first week but gains 1/4% on the true time during the second week. The time shown on Monday after two weeks will be

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Try yourself:There is an alloy (A) of silver and copper. A certain weight of this alloy is mixed with 15 kg of pure silver and is melted. The new alloy (B) contains 90% of silver. If alloy (A) is mixed with 10kg of a 90% silver alloy, and is melted to form new alloy (C), then (C) is found to contain 84% silver. Find the percentage of silver in (A).

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