1.3 Marks

The average weight of a class of students is 44 kg and the average weight ofanother class of students is 60 kg. Find the ratio of the number of students of thefirst class to the other class if the average weight of both the classes is 56 kg.

1) 11 : 15

2) 1 : 2

3) 1 : 3

4) 3 : 5

5) Cannot be determined

Solution:By alligation rule,

The average weight of the individual classes is 44 kg and 60 kg and the averageof both the combined classes is 56 kg.

Thus the ratio of the students = 4 : 12 = 1 : 3

Hence, option 3.

2.3 Marks

The average weight of boys is 52 kg and the average weight of girls is 40 kg andthe average weight of boys and girls together is 48 kg. If the numbers of boys is26, then find the numbers of girls.

1) 13

2) 18

3) 22

4) 35

5) 52

Solution:

By alligation rule,

Collapse All

Section I

∴ The ratio of girls to boys = 4 : 8 = 1 : 2

Let the number of girls be x,

∴ x : 26 = 1 : 2

∴ x = 13

Hence, option 1.

3.3 Marks

Kamlesh travels for 45 minutes at the speed of 62 km/hr. Further he travels for36 minutes at the rate of 80 km/hr. Find his average speed.

1) 66 km/hr

2) 70 km/hr

3) 71 km/hr

4) 74 km/hr

5) None of these

Solution:

By alligation rule,

The actual ratio is 45 : 36 = 5 : 4

The required ratio is 4 : 5.

Now divide the difference of both the speeds i.e. 62 and 80 in the ratio of 4 : 5.

So the average speed is 62 + 8 = 70 km/hr or 80 – 10 = 70 km/hr

Hence, option 2.

4.3 Marks

In what ratio should freely available water be mixed with the dilute HCL worth Rs.120 per litre so that after selling the mixture at Rs. 90 per litre, the profit will be50%?

1) 1 : 1

2) 1 : 2

3) 2 : 1

4) 5 : 4

5) 4 : 5

Solution:

Selling price of the mixture = Rs. 90

By alligation rule,

The required ratio is 1 : 1.

Hence, option 1.

5.3 Marks

Gopi purchased milk of two different types. In the first mixture, the ratio of milk towater is 3 : 14 and in the second mixture it is 8 : 9. He mixes the two givenmixtures and makes a third mixture of 30 litres in which the ratio of milk to wateris 6 : 11. Find the quantity of the first mixture (whose ratio is 3 : 14) required tomake 30 litres of the third kind of mixture.

1) 8 litres

2) 14 litres3) 18 litres

4) 16 litres

5) 12 litres

Solution:The fraction of milk in the different mixture is as follows:

Therefore,

Hence the ratio of the first mixture to the second mixture is 2 : 3.

Hence, option 5.

6.3 Marks

A cask was full of wine. A person used to draw out 25% of the wine from thecask and replace it with water. He repeated the same process 3 times and thusthere was only 135 litres of wine left in the cask and the rest of the jar was filledwith water. What was the initial amount of wine in the cask?

1) 265 litres

2) 280 litres

3) 300 litres

4) 320 litres

5) None of these

Solution:

Let the initial amount of wine in the cask be W, then

∴ W = 320 litres

∴ The initial amount of wine in the cask is 320 litre.

Hence, option 4.

7.3 Marks

1400 students took the TestFunda mock iCAT 01 in Mumbai. 74% of boys and88% of the girls cleared the cut-off in the online examination. If the totalpercentage of students qualifying is 80%, how many girls appeared for theexamination?

1) 400

2) 500

3) 600

4) 700

5) 800

Solution:

By alligation rule,

∴ The ratio of boys to girls is 4 : 3

Hence, option 3.

8.3 Marks

A man decides to travel 270 km in 6 hours partly by bike and partly by car. Thespeed of his bike was 60 km/h while that of his car was 30 km/h. What distancedid he travel by car?

1) 90 km

2) 120 km

3) 135 km

4) 180 km

5) 210 km

Solution:

Let the man travel for x hours on bike.

∴ Total distance travelled by the man on bike = 60x km

∴ Total distance travelled by the man by car = 30(6 – x) km

∴ 60x + 30(6 – x) = 270

∴ 60x + 180 – 30x = 270

∴ x = 30

∴ Total distance travelled by the man by car = 30(6 – 3) = 90 km

Hence, option 1.

9.3 Marks

A dishonest shopkeeper professes to sell pure sunflower oil at cost price, but hemixes it with another cheaper variety of oil and thereby gains 20%. Find thepercentage of the cheaper variety of oil in the mixture assuming that it isavailable for free.

1) 10%

2) 16.67%

3) 20%

4) 22.24%

5) 25%

Solution:

Let the C.P of 100 litres of pure sunflower oil be Rs. 100

∴ The S.P of 120 litres of pure sunflower oil is Rs. 120.

But since the shopkeeper gains 20%, he sells 120 litres of the mixture (sunfloweroil + cheaper variety of oil) at Rs. 120.

∴ Ratio of quantity of cheaper variety of oil to pure sunflower oil in the mixture

∴ The percentage of the cheaper variety of oil in the mixture

Hence, option 2.

10. If 8 men can cut a number of trees in 12 days by working 3 hours a day, for how

3 MarksIf 8 men can cut a number of trees in 12 days by working 3 hours a day, for howmany hours a day would 3 men have to work in order to cut thrice the number oftrees in 32 days?

1) 12 hours

2) 9 hours

3) 6 hours

4) 5 hours

5) 4 hours

Solution:

For x trees,

Work rate = 8 men

Time = 12 × 3 = 36 hours

∴ Work done = (8 × 36) men-hours

Later, work rate = 3 men

Time = (t × 32) hours

∴ Work done = (3 × t × 32) men-hours

∴ Time required by 3 men to cut 3x trees = 3 × 3 = 9 hours.

Hence, option 2.

11.3 Marks

If 45 women working 9 hours a day can do a piece of work in 18 days, in howmany days will 27 women working 6 hours a day do the same work?

1) 15 days

2) 24 days

3) 30 days

4) 36 days

5) 45 days

Solution:Work rate = 45 women

Time = (18 × 9) hours

∴ Work done = (45 × 18 × 9) women hours

Later, work rate = 27 women

Later, work rate = 27 women

Time = (d × 6) hours … (d = number of days)

Since work done is the same,

∴ 45 × 9 × 18 = 27 × 6 × d

d = 45 days

Hence, option 5.

12.3 Marks

In a blueberry eating competition, a certain number of women can eat a bucketfull of blueberries in 24 days. If there were 5 women less they would require 6days more. How many women are there?

1) 16

2) 25

3) 36

4) 20

5) 30

Solution:

Let there be x women.

∴ x women can eat a bucket full of blueberries in 24 days and (x – 5) womencan eat it in (24 + 6) = 30 days

∴ 24x = 30(x – 5)

∴ x = 25 women

Hence, option 2.

13.3 Marks

36 men can make 84 wood chairs in 10 hours. If 6 men leave the job how manychair will be made in 8 hours?

1) 72

2) 66

3) 60

4) 56

5) 48

Solution:36 men in 10 hours make 84 wood chairs i.e. work done by 36 men in 10 hoursis 84.

After 6 men leave, total number of men = 36 – 6 = 30

Let 30 men make x chairs in 8 hours.

∴ x = 56 chairs

Hence, option 4.

14.3 Marks

If 5 men can dig a well in 14 days by working 6 hours a day. What is the numberof men required to dig a well in 4 days by working 7 hours a day?

1) 15

2) 10

3) 12

4) 8

5) 6

Solution:

5 men working 6 hours a day can dig a well in 14 days.

Let x be required to dig a well in 4 days by working 7 hours a day.

∴ 5 × 14 × 6 = x × 4 × 7

∴ x = 15 men

Hence, option 1.

15.3 Marks

56 boys manufacture 256 toys in a day by working 8 hours; in how many dayscan 42 boys manufacture 840 toys by working 5 hours a day?

1) 2

2) 4

3) 7

4) 10

5) 14

Solution:

56 boys manufacture 256 toys in a day by working 8 hours

Let 42 boys manufacture 840 toys by working 5 hours a day, in x days

∴ 56 × 1 × 8 × 840 = 42 × x × 5 × 256

∴ x = 7 days

Hence, option 3.

16.3 Marks

15 men can do a piece of work in 28 days. How many men are needed to do thework in 7 days?

1) 30 men

2) 60 men

3) 75 men

4) 45 men

5) 90 men

Solution:

15 men can do a piece of work in 28 days.

∴ M1 = 15, D1 = 28 days

Let x be the number of men needed to do the same work in 7 days.

∴ M2 = x, D2 = 7 days

∵ Work done by 15 men in 28 days = Work done by x men in 7 days

∴ M1 × D1 = M2 × D2

∴ 15 × 28 = x × 7

∴ x = 60 men

Hence option 2.

17.3 Marks

Sachin alone can do a piece of work in 15 days. Vinod alone can do it in 24days. They work together for the entire duration of the work. If the total wages forthe work is Rs. 156, how much should Sachin be paid?

1) Rs. 64

2) Rs. 72

3) Rs. 82

4) Rs. 90

5) Rs. 96

Solution:

Sachin alone can do the work in 15 days.

Vinod alone can do the same work in 24 days.

Hence, option 5.

18.3 Marks

If 14 men and 22 women can do a piece of work in 5 days, in how many dayscan the work be done by 7 men and 11 women working together?

1) 7

2) 8

3) 10

4) 14

5) Cannot be determined

Solution:

14 men and 22 women can do a piece of work in 5 days.

If m and w are the number of days taken by a man and a woman to finish thework,

Then,

∴ 7 men and 11 women can finish the work in 10 days.

Hence, option 3.

Hence, option 3.

19.3 Marks

Rajni and Samira undertake to do a piece of work for Rs. 4000. Rajni alone cando it in 8 days and Samira alone can do it in 12 days. With the help of Radhikathey finish it in 3 days. How much should Radhika be paid for her contribution?

1) Rs. 800

2) Rs. 1500

3) Rs. 1333

4) Rs. 2000

5) Rs. 2500

Solution:

Rajni alone can do the work in 8 days.

Samira alone can do the work in 12 days.

Let Radhika alone can do the work in x days.

Hence, option 2.

20.3 Marks

Karan is twice as good as Rajan. Together, they finish the work in 42 days. Inhow many days can Karan alone do the same work?

1) 48

2) 56

2) 56

3) 63

4) 72

5) 84

Solution:

Let Rajan finish the work in 2x days.

Karan is twice as good as Rajan.

∴ Karan finishes the work in x days.

∴ x = 63 days

∴ Karan alone do the work in 63 days.

Hence, option 3.

21.3 Marks

In a hospital there is sufficient food for its 450 patients for 30 days. After 20days, 200 patients are discharged from the hospital and no new ones areadded. For how many extra days will the rest of the food last for the remainingpatients if each patient consumed the same amount of food?

1) 7 days

2) 1 day

3) 6 days

4) 8 days

5) 3 days

Solution:Total food available for 450 patients for 30 days = 450 × 30 units

Total food consumed by 450 patients in 20 days = 450 × 20 units

Food remaining = 450 × 10 units

Number of patients remaining = 250

∴ Number of extra days = 18 – 10 = 8 days

Hence, option 4.

22.3 Marks

During a severe draught, a society of 140 members had sufficient water storedfor 90 days. After 50 days 20 new members joined the society. For how manydays after the 20 new members joined the society would the rest of the water besufficient assuming everyone consumed the same amount of water?

1) 22 days

2) 25 days3) 28 days

4) 32 days

5) 35 days

Solution:

Total water available for 140 members for 90 days = 140 × 90 units

Total available consumed by 140 members in 50 days = 140 × 50 units

Water available after 50 days = 140(90 – 50) = 140 × 40 units

Number of members after 50 days = 160

Hence, option 5.

23.3 Marks

One tap can fill a tank in 8 hours and another can empty the tank in 20 hours. Athird tap is also connected to the tank. If all the three taps are opened together,the tank is filled in 15 hours. At what rate does the third pipe work?

1) Fills the tank in 12 hours

2) Empties the tank in 40 hours

3) Fills the tank in 60 hours

4) Empties the tank in 60 hours

5) Empties the tank in 120 hours

Solution:

Let the third tap fill the tank in x hours.

∴ The third pipe empties the tank in 120 hours.

Hence, option 5.

24.3 Marks

There are three pipes A, B and C in a tank. If all the pipes are open together, atank can be filled in 6 hours. If pipe A can fill the tank in 15 hours and pipe B can

fill the tank in 12 hours then at what rate does pipe C work?

1) Fills the tank in 12 hours

2) Empties the tank in 40 hours

3) Fills the tank in 60 hours

4) Empties the tank in 60 hours

5) Fills the tank in 90 hours

Solution:

Let pipe C can fill the tank in x hours.

∴ Pipe C fills the tank in 60 hours.

Hence, option 3.

25.3 Marks

Anand and Shiva can complete a piece of work in 18 days and 22 daysrespectively. They begin the work together, but Shiva leaves after some daysand Anand finishes the remaining work in 14 days. After how many days didShiva leave?

1) 14 days

2) 35.5 days

2) 35.5 days

3) 6.6 days

4) 2.2 days

5) 18 days

Solution:

Anand works alone for 14 days.

i.e. Shiva left after 2.2 days.

Hence, option 4.

26.3 Marks

Ajay completes 1/4 of a certain job in 5 days. Chandu completes 3/5 of the samejob in 9 days and Pankaj completes 7/10 of that job in 17.5 days. All of themwork together for 5 days and then Ajay and Chandu quit. How long will it take forPankaj to complete the remaining work alone?

1) 5.4 days

2) 2.5 days

3) 3.33 days

4) 5 days

5) 6.33 days

Solution:

∴ Total time taken by Ajay to complete the job = 4 × 5 = 20 days

Hence, option 1.

27.3 Marks

Yogesh can do a job in 3 days, Sandip can do the same job in 10 days andVishal can do the same job in 15 days. In how many days they will finish the worktogether?

1) 2 days

2) 3.5 days

3) 4 days

4) 5.5 days

5) 6 days

Solution:

Hence, option 1.

28.3 Marks

A contractor undertakes to dig a canal 10 km long in 180 days and employs 40men. After 60 days he finds that only 2.5 km of the canal has been completed. Tocomplete the work on the scheduled time how many men does he have toincrease?

1) 10

2) 20

3) 25

4) 15

5) 5

Solution:In 60 days 40 men completed 2.5 km of the canal.

Let x number of men be required to complete 10 – 2.5 = 7.5 km of the canal in180 – 60 = 120 days.

∴ M1 × D1 × W2 = M2 × D2 × W1

∴ 60 × 40 × 7.5 = x × 120 × 2.5

∴ x = 60 men

So the contractor requires 60 – 40 = 20 more men to complete the work on thescheduled time.

Hence, option 2.

29.3 Marks

P is twice as efficient as Q and R is thrice as efficient as P. What is the ratio ofthe number of days taken by P, Q and R, when they work individually?

1) 6 : 3 : 1

2) 3 : 1 : 6

3) 2 : 1 : 6

4) 3 : 6 : 1

5) 2 : 6 : 1

Solution:Ratio of efficiency of P, Q, R = 2 : 1 : 6

Hence, option 4.

30.3 Marks

Rahul is thrice as efficient as Ashish and together they do the same work in asmuch time as Ram and Raj together. If Ram and Raj can complete the work in 12

much time as Ram and Raj together. If Ram and Raj can complete the work in 12days and 20 days respectively, working alone, then in how many days will Rahulcomplete the work individually?

1) 5 days

2) 10 days

3) 15 days

4) 20 days

5) 30 days

Solution:

Ram and Raj working alone can complete the work in 12 days and 20 daysrespectively.

Let Ashish alone complete the same work in 3x days.

∴ Rahul alone can complete the work in x days.

∴ x = 10 days

Hence, option 2.

31.3 Marks

An inlet pipe can fill the tank in 7 hours and an outlet pipe can empty the sametank in 31.5 hours, working individually. How many additional number of outletpipes of the same capacity are required to be opened, so that the tank neverover flows?

1) 3

2) 4

3) 5

4) 6

5) 8

Solution:The inlet pipe is 4.5 times as efficient as the outlet pipe.

∴ In order for the tank to not overflow, required number of outlet pipes = 5

So we need only 4 more (5 – 1 = 4) outlet pipes.

Hence, option 2.32.

32.3 Marks

Pipe A takes 2/3 of the time required by pipe B to fill an empty tank individually.

When an outlet pipe C is also opened simultaneously with pipe A and pipe B, ittakes 2/3 more time to fill the empty tank than it takes, when only pipe A andpipe B are opened together. If it takes 24 hours to fill the tank when all the three

pipes are opened simultaneously, then in what time will pipe C empty the full tankoperating alone?

1) 12 hours

2) 24 hours

3) 30 hours

4) 36 hours

5) 42 hours

Solution:

Let pipe A fill the tank in 2x hours and pipe B fill it in 3x hours.

∴ C = 3x

i.e. In 3x hours pipe C can empty the whole tank.

∵ 2x = 24

∴ x = 12

∴ 3x = 3 × 12 = 36 hours

Hence, option 4.

33.3 Marks

1) a + b + c

2)

3)

4)

5)

Solution:

Hence, option 3.

34.3 Marks

1) p + q + r + s

2) p − q − r + s

3) p + q + r

4) p + q − r − s

5) None of these

Solution:

p, q, r and s are in proportion.

= s − q − r + p … [From (i)]

Hence, option 2.

35.3 Marks

1)

2)

3)

4)

5) None of these

Solution:

Using Componendo and Dividendo operation,

Using Invertendo operation,

Hence, option 1.

36.3 Marks

Zinc and copper are mixed in proportions 3 : 5 and 7 : 9 to form alloys A and B

respectively. If equal quantities of the two alloys are melted to form a third alloy C, theproportion of zinc and copper in C will be:

1) 9 : 11

2) 7 : 11

3) 11 : 19

4) 15 : 19

5) 13 : 19

Solution:

Consider 16 kg of alloy C

Hence, option 5.

37.3 Marks

A factory employs engineers, clerks and unskilled workers in the proportion 12 :7 : 3, and the wages of engineers, clerks and unskilled workers are in the ratio 6: 5 : 2. When 28 clerks are employed, the total daily wages of all amount to Rs.5424. The wages paid to each category is:

1) Rs. 3872, Rs. 1840 and Rs. 324

2) Rs. 3240, Rs. 1560 and Rs. 288

3) Rs. 3456, Rs. 1680 and Rs. 288

4) Rs. 2868, Rs. 1420 and Rs. 256

5) Rs. 2456, Rs. 1260 and Rs. 196

Solution:

Number of engineers, clerks and unskilled workers in the factory are 12x, 7x and3x respectively.

It is known that 28 clerks are employed.

∴ 7x = 28

∴ x = 4

∴ Total number of engineers = 48

Total number of unskilled workers = 12

Also, wages are in the ratio 6 : 5 : 2

∴ Total wages of all the employees = 48 × 6y + 28 × 5y + 12 × 2y = 452y

∴ 452y = 5424

∴ y = 12

∴ y = 12

The wages paid to engineers = 48 × 6 × 12 = Rs. 3456

The wages paid to graduates = 28 × 5 × 12 = Rs. 1680

The wages paid to unskilled workers = 12 × 2 × 12 = Rs. 288

Hence, option 3.

38.3 Marks

A bag contains 25 paise, 50 paise and 1 Re. coins. There are 188 coins in alland the total amount in the bag is Rs. 138. If there are four times as many 1 Re.coins as there are 50 paise coins, then what is the number of 25 paise coins?

1) 28

2) 48

3) 68

4) 82

5) 112

Solution:

Let the number of 50 paise coins in the bag = x

∴ The number of 1 Re. coins = 4x

∴ The number of 25 paise coins = 188 – 5x

∴ x = 28

∴ The number of 25 paise coins = 188 – 28 × 5 = 188 – 140 = 48

Hence, option 2.

39.3 Marks

A precious stone weighting 42 grams worth Rs. 21168 accidentally breaks intotwo pieces having weights in the ratio of 5 : 9. If the price varies as the square ofthe weight, then find the loss incurred.

1) Rs. 8640

2) Rs. 9720

3) Rs. 5420

4) Rs. 3590

5) Rs. 10430

Solution:The price varies as the square of the weight.

∴ P ∝ w2

∴ P ∝ w2

P = kw2

∴ 21168 = k × 422

Let the price of the stone of weight 15 gm and 27 gm be P15 and P27

respectively.

∴ P15 = 152 × 12 = Rs. 2700

∴ P27 = 272 × 12 = Rs. 8748

∴ Total loss incurred = 21168 – 2700 – 8748 = Rs. 9720

Hence, option 2.

40.3 Marks

In two alloys, silver and platinum in the ratios of 3 : 2 and 1 : 4. After alloyingtogether 15 kg of the first alloy, 25 kg of second and several kilograms of puresilver, an alloy was obtained in which the ratio of silver to platinum was 2 : 1. Findthe weight of the new alloy.

1) 45 kg

2) 60 kg

3) 66 kg

4) 78 kg

5) 84 kg

Solution:

∴ Total weight of platinum in the new alloy = 6 + 20 = 26 kg

But in the new alloy the ratio of silver to platinum is = 2 : 1

∵ Weight of platinum = 26 kg

∴ Weight of the silver = 52 kg

∴ Weight of the silver = 52 kg

∴ The weight of the new alloy = 52 + 26 = 78 kg

Hence, option 4.