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Arithmetic Version – 1.1

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Hi,

I am glad to see that you have started your preparation for CAT 2015. Work hard and you shall

succeed. Remember the key to success in an exam like CAT has little to with intelligence or to

do with hard work. It is about discipline. Even if you study couple of hours a day regularly, rest

assured you will do well in CAT.

In this PDF, you will find questions on Arithmetic. These questions were sent as doubts by

students. Some of these questions might be harder than the actual CAT questions. The idea

behind these solved examples is to build your concepts.

Below every question, you will find a link to the video solution of the question. Before watching

the video solution, please try to solve the questions on your own first. Hope you learn from it.

In case you face a problem or have some doubts, please post them on the course feed.

Alternatively, you can also mail your doubts on handakafunda@gmail.com

I look forward to hearing from you.

Cheers,

Ravi Handa

09765142632

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1. Abhinav leaves Mumbai at 6 am and reaches Bangalore at 10 am. Praveen leaves

Bangalore at 8 am and reaches Mumbai at 11:30 am. At what time do they cross each

other?

(a) 10 am (b) 8:32 am (c) 8:56 am (d) 9:20 am

Video solution : https://www.wiziq.com/tutorial/643005-Solved-Example-TSD-1

2. A, B and C started out on a journey to a place which was 120 km away. A and B went by

car at the speed of 50 km/hr while C travelled by Tonga at 10 km/hr. After a certain

distance B got off and travelled the rest distance by another Tonga at 10 km/hr, while A

went back for C and reached the destination at the same time as B arrived. The no of

hours required for the trip was:

(a) 4h (b) 5h (c) 4.8h (d) CBD

Video Solution : https://www.wiziq.com/tutorial/643171-Solved-Example-TSD-2

3. A man goes to a fair with his son and dog. Unfortunately the man misses his son which

he realizes 20 minutes later. The son comes back towards his home at the speed of

20m/min and the man follows him at 40m/min. The dog runs to the son and comes back

to the man and it keeps moving to and fro at 60m/min between son and man till they

meet. What is the distance travelled by dog in the direction of the son?

(a) 800m (b) 1675m (c) 848m (d) 1000m

Video Solution : https://www.wiziq.com/tutorial/643174-Solved-Example-TSD-3

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4. Sunil leaves for his office at the same time everyday. If Sunil walks at 10 kmph he

reaches his office 4 min early. If he walks at 5 kmph he reaches 2 min late. Determine

the speed with which he should walk so as to reach on time. Also, find the distance to

his office.

(a) 6 kmph, 1 km (b) 6 kmph, 0.8 km

(c) 6.33 kmph, 0.8 km (d) 7.5 kmph, 1 km

Video Solution : https://www.wiziq.com/tutorial/643168-Solved-Example-TSD-4

5. Priya’s school usually gets over at 5 pm. Her father drives from home to pick her up,

reaching the school exactly at 5 pm. One day, a half-holiday is announced and the school

finishes for the day at 2 pm. Rather than sitting and waiting, Priya decided to start

walking towards home. Her father meets her along the way and as a result they reach

home an hour earlier than normal. What is the ratio of Priya’s walking speed to her

father’s driving speed?

(a) 1 : 4 (b) 1 : 5 (c) 1 : 2 (d) 1 : 8

Video Solution : https://www.wiziq.com/tutorial/643178-Solved-Example-TSD-5

6. Vinay fires two bullets from the same place at an interval of 12 minutes but Raju sitting

in a train approaching the place hears the second report 11 minutes 30 seconds after

the first. What is the approximate speed of train (if sound travels at the speed of 330

metre per second)?

(a)330/12 (b) 330/23 (c) 330/25 (d) 330/24

Video Solution : https://www.wiziq.com/tutorial/643180-Solved-Example-TSD-6

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7. Shatabdi Express had a engine trouble and hence its speed got reduced to 2/3 rd of

normal speed. It reached the destination at 5:12 pm. Had the engine trouble occurred

48 km further on, the train would have reached at exactly 5 pm. What is the normal

speed of the train?

(a) 120 (b) 100 (c) 80 (d) 60

Video Solution : https://www.wiziq.com/tutorial/643185-Solved-Example-TSD-7

8. In a race of 1 km, A gives B a start of 100 m and still wins the race by 20 seconds. But if A

gives B a start of 25 seconds, B wins by 50 meters. Find the time taken by A to run 1 km.

(a) 17 Seconds (b) 500/29 Seconds (c) 1200/29 Seconds (d) 700/29 Seconds

Video Solution : https://www.wiziq.com/tutorial/732814-Solved-Example-Arithmetic-13-Time-

Speed-and-Distance

9. Cars A and B are travelling on two perpendicular roads towards city X with equal speeds.

Car A starts from a distance of 100 km at 11 am while car B starts from a distance of 70

km at 12 noon. At 2 pm the two cars are 50 km apart. What are their speeds?

(a) 15 kmph (b) 20 kmph (c) 25 kmph (d) 30 kmph

Video Solution : https://www.wiziq.com/tutorial/738670-Solved-Example-Arithmetic-14-Time-

Speed-and-Distance

10. Fresh Grapes contain 90% water by weight while dried grapes contain 20% water. What

is the weight of dry grapes available from 20Kg of fresh grapes?

(a) 2 Kg (b) 2.4 Kg

(c) 2.5 Kg (d) None of these

Video Solution : https://www.wiziq.com/tutorial/977640-solved-example-arithmetic-10-

percentage

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11. In a factory, 80% of the employees are males. Among them 20% are matriculates and

the remaining are graduates. Among the females, 25% are matriculates and remaining

are graduates. If the total number of female’s employees in the factory are 600, how

many graduates are there in the factory?

(a) 1940 (b)1986 (c) 2370 (d)3000

Video Solution : https://www.wiziq.com/tutorial/977633-solved-example-arithmetic-11-

percentage

12. Ramesh owns a plot worth Rs 10000/- which he sold to Mukesh at a profit of 10%. Later

Mukesh sold it back to Ramesh at a loss of 10%. In the overall deal, Ramesh

(a) Lost Rs 100/-

(b) Lost Rs 900/-

(c) Gained Rs 100/-

(d) Gained Rs 1100/-

Video Solution : https://www.wiziq.com/tutorial/977637-solved-example-arithmetic-12-profit-

and-loss

13. 600 men were seized in a garrison town with provisions for 35 days allowing each man

18 ozs. per day. How long would the provisions last if the garrisons were reinforced by

300 men and the daily allowance was reduced to 15 ozs. per day?

(a) 25 (b) 28 (c) 40 (d) None of these

Video Solution : https://www.wiziq.com/tutorial/731302-Solved-Example-Arithmetic-12-Time-

and-Work

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14. A shipping clerk has five boxes of different but unknown weights each weighing less

than 100 kg. The clerk weights the boxes in pairs. The weights obtained are 110, 112,

113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight of the heaviest box?

a) 60 kg b) 65 kg c) 64 kg d) 62 kg

Video Solution : https://www.wiziq.com/tutorial/644986-Solved-Example-Average-1

15. A, B, C are three, pipes connected to a tank such that 6 times the time taken by A to fill

the tank is 7 times the time taken by B and C together to fill the tank, while 3 times the

time taken by C to fill the tank is 10 times the time taken by A and B together to fill the

tank. If A, B, C together fill the tank is 60/13 hours then find the time taken by B alone.

Video Solution: https://www.wiziq.com/tutorial/963007-solved-example-arithmetic-time-and-

work-pipes

16. A can do a piece of work in 15 days and B in 20 days. How much time will they take to

complete the work, if they work on alternate days, starting with A?

Two taps A and B can fill a tank in 20 min & 30 min respectively. An outlet pipe C can

empty the full tank in 15 min. A, B and C are opened alternatively. , each for 1 min.

How long will the tank take to be filled?

Video Solution: https://www.wiziq.com/tutorial/967653-solved-example-arithmetic-time-and-

work-alternating-workers

17. Ram, Suresh and Shilpa, Working together, can do a piece of work in 1 day. Ram is thrice

as efficient as Suresh, and Suresh takes twice the number of days as Shilpa takes to do it

alone. What is the difference between the number of days taken by Ram and Shilpa,

each working alone, to complete the work?

A) 1

B) 2

C) 3

4) 4

5) 5

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Video Solution: https://www.wiziq.com/tutorial/967654-solved-example-arithmetic-time-and-

work-3-people-working

18. X, Y and Z are three quantities.

X varies inversely with Y when Z is constant.

Y varies inversely with Z when X is constant.

When Y=8 and Z=7, X=30. Find X if Y=16 and Z=21

Video Solution: https://www.wiziq.com/tutorial/968655-arithmetic-solved-example-

proportionality

19. 1. There are two mixtures of honey and water, the quantity of honey in them being 25%

and 75% of the mixture.

If 2 gallons of the first are mixed with three gallons of the second , what will be the ratio

of honey to water in new mixture?

a. 11:2 b.11:9 c. 9:11 d. 2:11

2. There are two kinds of alloys of tin and copper. The first alloy contains tin and copper

such that 93.33% of itis tin. In the second alloy there is 86.66% tin. What weight of the

first alloy should be mixed with some weight of the second alloy so as to make a 50kg

mass containing 90% of tin?

a. 15kg b.30kg c.20kg d. 25kg

3. A vessel is full of a mixture of kerosene and petrol in which there is 18% kerosene.

Eight liters are drawn off and then the vessel is filled with petrol. If the kerosene is now

15%, how much does the vessel hold?

a.40lt b.32lt c. 36 lt d. 48lt

Video Solution: https://www.wiziq.com/tutorial/969198-solved-example-arithmetic-mixtures-

and-alligation

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20. There are two milk water solutions S1 and S2. The ratio of milk:water in them is 2:3 and

4:5 They are mixed in the ratio of 6:7 and the resulting mixture is sold at 30 Rs. per liter.

If the cost of milk is 40 Rs. per liter, then what is the profit percentage?

a) 72 b) 71.68 c) 70.83 d) 76.92

Video Solution: https://www.wiziq.com/tutorial/970531-solved-example-arithmetic-mixtures

21. A group of soldiers are marching with a speed of 5m/sec.The distance between the first

and the last row of soldiers is 100 m.A dog starts running from the last row and moves

towards the first row,turns and comes back to the last row.If the dog has travelled 400

m,the speed of the dog is:

a) 5 b) 5 sqrt(2) c) 10 d) None of these

Video Solution: https://www.wiziq.com/tutorial/971008-solved-example-arithmetic-time-

speed-distance-dog-soldiers

22. A 20 litre vessel is filled with alcohol. Some of the alcohol is poured out into another

vessel of an equal capacity, which is then completely filled by adding water. The mixture

thus obtained is then poured into the first vessel to capacity. Then 20/3 litres is poured

from the first vessel into the second. Both vessels now contain an equal amount of

alcohol.

How much alcohol was originally poured from the first vessel into the second?

(a) 9 litres (b) 10 litres (c) 12 litres (d) 12.5 litres

Video Solution: https://www.wiziq.com/tutorial/971010-solved-example-arithmetic-mixtures-

two-vessels-transfer

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