### Find solutions for all the questions at the end of each set:

### Set A

1.The average speed of a tractor is two–fifths the average speed of a car. The car covers 450 km in 6 hours. How much distance will the tractor cover in 8 hours?

(1) 210km

(2) 240 km

(3) 420km

(4) 480 km

2.The area of a square is four times the area of a rectangle. The length of the rectangle is 25 cm and its breadth is one cm less than one–fifth of its length. What is the perimeter of the square?

(1) 80 cm

(2) 60 cm

(3) 160 cm

(4) Cannot be determined

3.What value will be obtained if the square of 22 is subtracted from the cube of 12?

(1) 1244

(2) 1344

(3) 1454

(4) 1354

4.The marks of six boys in a group are 48, 59, 87, 37, 78 and 57. What are the average marks of all six boys?

(1) 62

(2) 64

(3) 61

(4) 63

(5) None of these

5.The ratio of the present ages of Tarun and Varun is 3 : 7. After 4 years Varan’s age will be 39 years. What was Tarun’s age 4 years ago?

(1) 12 years

(2) 13 years

(3) 11 years

(4) 18 years

6.The sum of five consecutive even numbers is equal to 170. What is the sum of the second largest number and the square of the smallest number amongst them together?

(1) 936

(2) 932

(3) 938

(4) 934

7.How many sacks are required for filling 1026 kg of rice if each sack is filled with 114 kg of rice?

(1) 19

(2) 15

(3) 7

(4) 9

8.Ravi consistently runs 350 metres every day except on Tuesdays when he runs 500 metres. How many kilometres will he run in two weeks? (In this question the week starts from Monday.)

(1) 4.5 km

(2) 4.8 km

(3) 5.2km

(4) 5.4 km

9.The simple interest accrued in 3 years on a principal of `25,000 is three–twentieths the principal. What is the rate of simple interest pcpa?

(1) 5

(2) 4

(3) 6

(4) 3

10.Sumit purchased an item for `6,500 and sold it at a gain of 24%. From that amount he purchased another item and sold it at a loss of 20%. What is his overall gain/loss?

(1) Loss of 42

(2) Gain of 42

(3) Loss of 52

(4) Neither gain nor loss

Answer Key:

1. 2; Average speed of the car = = 75 km/h

Average speed of the tractor = 75 × =30 km/h

Distance covered by the tractor = 30 × 8 = 240 km

2. 1; Length of the rectangle = 25 cm

Breadth of the rectangle = –1 = 4 cm

Area of the rectangle = 25 × 4 = 100 sq cm

Area of the square = 4 × 100 = 400 sq cm

Side of the square = 20 cm

Perimeter of the square = 4 × 20 = 80 cm

3. 1; (12)3 – (22)2 = 1728 – 484 = 1244

4. 3; = 61

5. 3; Varun’s present age = 39 – 5 = 35 years

So, Tarun’s present age = 15 years

Tarun’s age 4 years ago = 11 years

6. 1; Let the numbers be x, x + 2, x + 4, x+6 and x + 8.

According to the question,

x + x + 2 + x + 4 + x + 6 + x + 8=170

or 5x + 20 = 170

or x + 4 = 34

or x = 30.

Second largest No. = 30 + 6 = 36

Square of smallest No. = 900

Sum of these Nos. = 900 + 36 = 936

7. 4;

8. 3;

9. 1; I = 25000 × = 3750, r = = 5%

10. 3; Second selling price = 6500 × = 6448

Loss = 6500 – 6448 = 52

### Find solutions for all the questions at the end of each set:

### Set B

### 1. A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then, the number of papers in which he got more than 50% marks is

### (a) 1

### (b) 3

### (c) 4

### (d) 5

### 2. 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) 300

### (b) 250

### (c) 400

### (d) 500

### 3. Forty percent of the employees of a certain company are men and 75% of the men earn more than Rs 25,000 per year. If 45% of the company's employees earn more than Rs 25,000 per year, what fraction of the women employed by the company earn Rs 25,000 per year ?

### (a) 2/11

### (b) 1/4

### (c) 1/3

### (d) 3/4

### 4. In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals : I, II and III, 50% of those asked favoured proposal I, 30% favoured proposal II and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what percentage of those asked favoured more than one of the three proposals ?

### (a) 10

### (b) 12

### (c) 17

### (d) 22

### 5. One bacteria splits into eight bacteria of the next generation. But due to environment, only 50% of one generation can produce the next generation. If the seventh generation number is 4096 million, what is the number in first generation ?

### (a) 1 million

### (b) 2 million

### (c) 4 million

### (d) 8 million

### 6. I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more what I had paid. What per cent of the total amount paid by me was paid for the pens ?

### (a) 37. 5%

### (b) 62.5%

### (c) 50%

### (d) None of these

### 7. A man earns x% on the first Rs 2,000 and y % on the rest of his income. If he earns Rs 700 from Rs 4,000 and Rs 900 from Rs 5,000 of income, find x%.

### (a) 20%

### (b) 15%

### (c) 25%

### (d) None of these

### 8. The price of a Maruti car rises by 30% while the sales of the car comes down by 20%. What is the percentage change in the Total revenue ?

### (a) - 4%

### (b) - 2%

### (c) + 4%

### (d) + 2%

### 9. A person who has a certain amount with him goes to market. He can buy 50 oranges or 40 mangoes. He retains 10% of the amount for taxi fares and buys 20 mangoes and of the balance, he purchases oranges. Number of oranges he can purchase is

### (a) 36

### (b) 40

### (c) 15

### (d) 20

### 10. 2/5 of the voters promise to vote for P and the rest promised to vote for Q. Of these, on the last day 15% of the voters went back their promise to vote for P and 25% of voters went back of their promise to vote for Q, and P lost by 2 votes. Then, the total number of voters is

### (a) 100

### (b) 110

### (c) 90

### (d) 95

### Solutions :

### 1. (c); Let the marks scored in five subjects be 6x, 7x, 8x, 9x and 10x

### Total marks in all the five subjects=40x

### Max marks of the five subjects=40x/0.6

### (∵ 40x is 60% of total marks)

### ∴ Max marks in each subject=40x/(0.6×5)=13.3 x

### Hence, percentage in each subject=6x/13.33x×100, 7x/13.33×100,8x/13.33x×100,(9x×100)/13.33x and (10x×100)/13.33x

### Or 45.01%, 52.51%, 60.01%, 67.51% and 75.01%.

### ∴ Number of papers in which he got more than 50% marks is 4.

### 2. (a); Let x be the number of people who were asked for donation.

### People already solicited=0.6 x,

### Remaining people=0.4 x

### Amount collected from the people solicited =600×0.6 x=360 x which is 75% of the amount to be collected. Remaining amount 25%=120 x.

### ∴ Average donation from remaining people=120x/0.4x=300

### 3. (d); Let number of man and women by 40 and 60 respectively.

### ∴ Number of men earning more than Rs. 25,000=30

### Total number of employees earning more then Rs. 25,000=45

### ∴ Number of women earning more than Rs. 25,000=(45-30)=Rs. 15

### Now, fraction of the women earning Rs. 25,000 or less=(60-15)/60=45/60=3/4

### 4. (c); Given,

### 45-(x+y)+25-(x+z)+15-(y+z)+(x+y+z+5)=78

### ⇒(x+y+z)=12

### ∴ Percentage of those asked favoured more than one proposal=12+5=17

### 5. (a); Let number of bacteria in the first generation be x.

### ∴ Number of bacteria in the second, third, fourth ……………generation would be

### 8(x/2),8(4x/2),8(16x/2)…………and so on.

### x,4x,16x,64x,…..it is a GP with common difference 4. Hence, seventh term of GP=x(4)^6=4096⇒x〖 (2)〗^12=4096

### x=1 or 1 million

### 6. (b); Let 5P+7P_C+4E_R=100………..(i)

### ∴6P+14P_C+8E_R=150 …………………..(ii)

### Multiplying Eq. (i) by 2, we get

### 10P+14P_C+8E_R=200 ………….(iii)

### Solving Eqs. (ii) and (iii) simultaneously, we get

### P=12.5.

### Hence, total amount paid for 5P=12.5×5=62.5

### and it is the required percentage.

### 7. (b); 2*x/100+2,000*y/100=700 …………..(i)

### And 2,000*x/100+3,000*y/100=900………….(ii)

### On simplifying these equations change to x+y=35 and 2x+3y=90. Solving these two equations simultaneously we get x=15%

### 8. (c); Let the original price and sale be 10 unit each. Then, original revenue collection=10×10=100

### New price=10×1.3=13, New sale=10×0.8=8

### New revenue collection=104.

### Hence, revenue is increased by 4%.

### 9. (d); Suppose the person has Rs. 100 with him.

### ∴ Price per orange is Rs. 2 and that of a mango is Rs. 2.50. After keeping Rs. 10 for taxi, he is left with Rs. 90.

### Price of 20 mangoes=Rs. 40. Remaining money =(90-40)=Rs. 50

### So, he can buy50/2.5=20 oranges for this amount.

### 10. (a); Let total number of votes polled by 100, then votes polled in favour of P=40-6+15=49

### Votes polled in favour of Q=60-15+6=51

### Difference=51-49=2. It is already given that P lost by 2 votes, hence total number of votes polled=100.

### Find solutions for all the questions at the end of each set:

### Set C

1. There are two containers of equal capacity. The ratio of milk to water in the first container is 3 : 1, in the second container is 5 : 2. If they are mixed up, then the ratio of milk to water in the mixture will be

(a) 28 : 41

(b) 41 : 28

(c) 15 : 41

(d) 41 : 15

2. Zinc and copper are in the ratio 5 : 3 in 400 g of an alloy. How much of copper (in g) should be added to make the ratio 5 : 4?

(a) 72

(b) 200

(c) 50

(d) 66

3. In a mixture of 60 L the ratio of acid and water is 2 : 1. If the ratio of acid and water is to be 1 : 2, then the amount of water (in litres) to be added to the mixture is

(a) 55

(b) 60

(c) 50

(d) 45

4. In two blends of mixed tea, the ratios of Darjeeling and Assam tea are 4 : 7 and 2 : 5. He ratio in which these two blends should be mixed to get the ratio of Darjeeling and Assam tea in the new mixture as 6 : 13 is

(a) 2 : 7

(b) 5 : 13

(c) 4 : 13

(d) 22 : 35

5. Two vessels A and B contain milk and water mixed in the ratio 8 : 5 and 5 : 2, respectively. The ratio in which these two mixtures be mixed to get a new mixture containing 69 3/13% milk is

(a) 3 : 5

(b) 5 : 2

(c) 5 : 7

(d) 2 : 7

6. 20 L of a mixture contains 20% alcohol and the rest water. If 4 L of water be mixed in it, the percentage water be mixed in it, the percentage of alcohol in the new mixture, will be

(a) 33 1/3%

(b) 16 2/3%

(c) 25%

(d) 12 1/2%

7. Pure milk costs 16/L. After adding water the milkman sells the mixture 15/L and thereby makes a profit of 25%. In what respective ratio does he mix milk with water?

(a) 3 : 1

(b) 4 : 3

(c) 3 : 2

(d) 5 : 3

8. The ratio of milk and water in mixtures of four containers are 5 : 32 : 1, 3 : 2 and 7 : 4, respectively. In which container is the quantity of milk, relative to water, minimum?

(a) First

(b) Second

(c) Third

(d) Fourth

9. A shopkeeper bought 15 kg of rice at the rate of Rs. 29 per kg and 25 kg of rice at the rate of Rs. 20 per kg. He sold the mixture of both types of rice at the rate of Rs. 27 per kg. His profit in this transaction is

(a) Rs. 125

(b) Rs. 150

(c) Rs. 140

(d) Rs. 145

10. A container contains 60 kg of milk. Form this container 6 kg of milk was taken out and replaced by water. This process was repeated further two times. The amount of milk left in the container is

(a) 34.24 kg

(b) 39.64 kg

(c) 43.74 kg

(d) 47.6 kg

Answer Key:

1. (d) 41 : 15

2. (c) 50

3. (b) 60

4. (d) 22 : 35

5. (d) 2 : 7

6. (b) 16 2/3%

7. (a) 3 : 1

8. (c) Third

9. (d) Rs. 145

10. (c) 43.74 kg

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