CAT Questions

In a flight of 600 km, an aircraft was slowed down due to bad weather

Time Distance

In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:

  1. 1 hour
  2. 2 hours
  3. 3 hours
  4. 4 hours

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It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car

Time Distance

It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:

  1. 2 : 3
  2. 3 : 4
  3. 4 : 3
  4. 3 : 2

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Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph

Time Distance

Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

  1. 9
  2. 10
  3. 12
  4. 20

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An express train travelling at 80 km/hr overtakes a goods train, twice as long

Time Distance

An express train travelling at 80 km/hr overtakes a goods train, twice as long and going at 40 km/hr on a parallel track, in 54 s. How long will the express train take to cross a platform of 400 m long?

  1. 18 s
  2. 27 s
  3. 36 s
  4. 45 s

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A chartered bus carrying office employees travels everyday in two shifts

Time Distance

A chartered bus carrying office employees travels everyday in two shifts - morning and evening. In the evening, the bus travels at an average speed which is 50% greater than the morning average speed; but takes 50% more time than the amount of time it takes in the morning. The average speed of the chartered bus for the entire journey is greater/less than its average speed in the morning by

  1. 18% less
  2. 30% greater
  3. 37.5% greater
  4. 50% less

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A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km

Time Distance

A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km/hr is?

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Arup and Swarup leave point A at 8 AM to point B

Time Distance

Arup and Swarup leave point A at 8 AM to point B. To reach B, they have to walk the first 2 km, then travel 4 km by boat and complete the final 20 km by car. Arup and Swarup walk at a constant speed of 4 km/hr and 5 km/hr respectively. Each rows his boat for 30 minutes. Arup drives his car at a constant speed of 50 km/hr while Swarup drives at 40 km/hr. If no time is wasted in transit, when will they meet again?

  1. At 9.15 AM
  2. At 9.18 AM
  3. At 9.21 AM
  4. At 9.24 AM
  5. At 9.30 AM

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Arun drove from home to his hostel at 60 miles per hour

Time Distance

Arun drove from home to his hostel at 60 miles per hour. While returning home he drove half way along the same route at a speed of 25 miles per hour and then took a bypass road which increased his driving distance by 5 miles, but allowed him to drive at 50 miles per hour along this bypass road. If his return journey took 30 minutes more than his onward journey, then the total distance traveled by him is

  1. 55 miles
  2. 60 miles
  3. 65 miles
  4. 70 miles

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A motorbike leaves point A at 1 pm and moves towards point B at a uniform speed

Time Distance

A motorbike leaves point A at 1 pm and moves towards point B at a uniform speed. A car leaves point B at 2 pm and moves towards point A at a uniform speed which is double that of the motorbike. They meet at 3:40 pm at a point which is 168 km away from A. What is the distance, in km, between A and B?

  1. 364
  2. 378
  3. 380
  4. 388

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X and Y can do a piece of work in 20 days and 12 days

Time Work

X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

  1. 6 days
  2. 10 days
  3. 20 days
  4. 15 days

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A and B can do a work in 8 days, B and C can do the same work in 12 days

Time Work

A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in

  1. 8 days
  2. 6 days
  3. 4 days
  4. 12 days

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A water tank has three taps A, B, and C. A fills four buckets in 24 mins

Time Work

A water tank has three taps A, B, and C. A fills four buckets in 24 mins, B fills 8 buckets in 1 hour and C fills 2 buckets in 20 minutes. If all the taps are opened together a full tank is emptied in 2 hours. If a bucket can hold 5 litres of water, what is the capacity of the tank?

  1. 60 litres
  2. 120 litres
  3. 180 litres
  4. 240 litres

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A group of workers was put on a job. From the second day onwards

Time Work

A group of workers was put on a job. From the second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in two-thirds the time. How many workers were there in the group?

  1. 2
  2. 3
  3. 5
  4. 11

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A and B together can do a piece of work in 30 days. A having worked for 16 days

Time Work

A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?

  1. 30 days
  2. 40 days
  3. 60 days
  4. 70 days

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A group of men decided to do a job in 8 days. But since 10 men dropped out

Time Work

A group of men decided to do a job in 8 days. But since 10 men dropped out every day, the job got completed at the end of the 12th day. How many men were there at the beginning?

  1. 80
  2. 90
  3. 165
  4. 175

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A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days

Time Work

A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?

  1. 18 days
  2. 24 days
  3. 30 days
  4. 36 days

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A and B can complete a work in 15 days and 10 days respectively

Time Work

A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in:

  1. 8 days
  2. 10 days
  3. 12 days
  4. 15 days

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Three machines, A, B and C can be used to produce a product

Time Work

Three machines, A, B and C can be used to produce a product. Machine A will take 60 hours to produce a million units. Machine B is twice as fast as Machine A. Machine C will take the same amount of time to produce a million units as A and B running together. How much time will be required to produce a million units if all the three machines are used simultaneously?

  1. 6 hours
  2. 8 hours
  3. 10 hours
  4. 12 hours

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Three small pumps and a large pump are filling a tank

Time Work

Three small pumps and a large pump are filling a tank. Each of the three small pump works at 2/3 the rate of the large pump. If all four pumps work at the same time, they should fill the tank in what fraction of the time that it would have taken the large pump alone?

  1. 2/3
  2. 1/3
  3. 4/7
  4. 3/4

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Two typists undertake to do a job. The second typist begins working

Time Work

Two typists undertake to do a job. The second typist begins working one hour after the first. Three hours after the first typist has begun working, there is still 9/20 of the work to be done. When the assignment is completed, it turns out that each typist has done half the work. How many hours would it take each one to do the whole job individually?

  1. 5 hr and 4 hr
  2. 12 hr and 8 hr
  3. 8 hr and 5.6 hr
  4. 10 hr and 8 hr

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A and B together can complete a piece of work in 35 days while A alone

Time Work

A and B together can complete a piece of work in 35 days while A alone can complete the same work in 60 days. B alone will be able to complete the same working in

  1. 74 days
  2. 80 days
  3. 84 days
  4. 90 days

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A tank is connected with both inlet pipes and outlet pipes

Time Work

A tank is connected with both inlet pipes and outlet pipes. Individually, an inlet pipe can fill the tank in 7 hours and an outlet pipe can empty it in 5 hours. If all the pipes are kept open, it takes exactly 7 hours for a completely filled-in tank to empty. If the total number of pipes connected to the tank is 11, how many of these are inlet pipes?

  1. 2
  2. 4
  3. 5
  4. 6

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Three carpenters P, Q and R are entrusted with office furniture work

Time Work

Three carpenters P, Q and R are entrusted with office furniture work. P can do a job in 42 days. If Q is 26% more efficient than P and R is 50% more efficient than Q, then Q and R together can finish the job in approximately

  1. 11 days
  2. 13 days
  3. 15 days
  4. 17 days

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Four two-way pipes A, B, C and D can either fill an empty tank

Time Work

Four two-way pipes A, B, C and D can either fill an empty tank or drain the full tank in 4, 10, 12 and 20 minutes respectively. All four pipes were opened simultaneously when the tank is empty. Under which of the following conditions the tank would be half filled after 30 minutes?

  1. Pipe A filled and pipes B, C and D drained
  2. Pipe A drained and pipes B, C and D filled
  3. Pipes A and D drained and pipes B and C filled
  4. Pipes A and D filled and pipes B and C drained
  5. None of the above

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A tank has an inlet pipe and an outlet pipe

Time Work

A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in 8 hours. If the outlet pipe is open then the inlet pipe fills the empty tank in 10 hours. If only the outlet pipe is open then in how many hours the full tank becomes half-full?

  1. 20
  2. 30
  3. 40
  4. 45

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Amal can complete a job in 10 days and Bimal can complete it in 8 days

Time Work

Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 days and are paid a total amount of Rs 1000 as remuneration. If this amount is shared by them in proportion to their work, then Kamal's share, in rupees, is

  1. 100
  2. 200
  3. 300
  4. 400

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8 litres are drawn from a cask full of wine and is then filled with water

Mixtures Alligation

8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 65. How much wine did the cask hold originally?

  1. 18 litres
  2. 42 litres
  3. 32 litres
  4. 24 litres

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Fresh grapes contain 90% water while dry grapes contain 20% water

Mixtures Alligation

Fresh grapes contain 90% water while dry grapes contain 20% water. What is the weight of dry grapes obtained from 20 kg fresh grapes?

  1. 2 kg
  2. 2.4 kg
  3. 2.5 kg
  4. 10 kg

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A can contains a mixture of two liquids A and B is the ratio 7:5

Ratio Proportion Mixtures Alligation

A can contains a mixture of two liquids A and B is the ratio 7:5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many litres of liquid A was contained by the can initially?

  1. 10
  2. 20
  3. 21
  4. 25

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A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup

Mixtures Alligation

A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

  1. 1/4 
  2. 1/3
  3. 1/7
  4. 1/5

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In what ratio must a grocer mix two varieties of tea worth Rs.60 a kg and Rs.65 a kg

Mixtures Alligation

In what ratio must a grocer mix two varieties of tea worth Rs.60 a kg and Rs.65 a kg so that by selling the mixture at Rs.68.20 a kg, he may gain 10%?

  1. 3 : 2
  2. 3 : 5
  3. 3 : 4
  4. 4 : 5

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The milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively

Mixtures Alligation

The milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively. In what ratio the liquids in both the vessels be mixed to obtain a new mixture in vessel C consisting half milk and half water?

  1. 8 : 3
  2. 4 : 3
  3. 2 : 3
  4. 7 : 5

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A man invests Rs. 3,000 at the rate of 5% per annum. How much more should he invest

Mixtures Alligation Interests

A man invests Rs. 3,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?

  1. Rs. 1,200
  2. Rs. 1,500
  3. Rs. 1,700
  4. Rs. 2,000

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A jar contains a mixture of two liquids A and B in the ratio 4:1

Mixtures Alligation

A jar contains a mixture of two liquids A and B in the ratio 4:1. When 10 litres of the liquid B is poured into the jar, the ratio becomes 2:3. How many litres of liquid A were contained in the jar?

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Nine litres of solution are drawn from a cask containing water

Mixtures Alligation

Nine litres of solution are drawn from a cask containing water. It is replaced with a similar quantity of pure milk. This operation is done twice. The ratio of water to milk in the cask now is 16:9. How much does the cask hold?

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There are two containers A and B of milk solution. The ratio of milk and water

Mixtures Alligation

There are two containers A and B of milk solution. The ratio of milk and water in container A is 3 : 1 and in container B, it is 4 : 1. How many liters of container B solution has to be added to 20 lts of container A solution such that in the resulting solution the ratio of milk to water should be 19 : 6?

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There are two alloys P and Q made up of silver, copper and aluminium

Mixtures Alligation

There are two alloys P and Q made up of silver, copper and aluminium. Alloy P contains 45% silver and rest aluminum. Alloy Q contains 30% silver, 35% copper and rest aluminium. Alloys P and Q are mixed in the ratio of 1 : 4.5. The approximate percentages of silver and copper in the newly formed alloy is

  1. 33% and 29%
  2. 29% and 26%
  3. 35% and 30%
  4. None of the above

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Bottle 1 contains a mixture of milk and water in 7: 2 ratio

Mixtures Alligation

Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water in 9 : 4 ratio. In what ratio of volumes should the liquids in Bottle 1 and Bottle 2 be combined to obtain a mixture of milk and water in 3 : 1 ratio?

  1. 27 : 14
  2. 27 : 13
  3. 27 : 16
  4. 27 : 18

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Consider three mixtures - the first having water and liquid A in the ratio 1:2

Mixtures Alligation

Consider three mixtures - the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1: 3, and the third having water and liquid C in the ratio 1 : 4. These three mixtures of A, B, and C, respectively, are further mixed in the proportion 4 : 3 : 2. Then the resulting mixture has

  1. The same amount of water and liquid B
  2. The same amount of liquids B and C
  3. More water than liquid B
  4. More water than liquid A

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The surface area of a sphere is 616 square cm

Mensuration

The surface area of a sphere is 616 square cm. If its radius is changed so that the area gets reduced 75% then the radius becomes

  1. 1.6 cm
  2. 2.3 cm
  3. 2.5 cm
  4. 3.5 cm

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50 men took a dip in a water tank 40 m long and 20 m broad on a religious day

Mensuration

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be

  1. 20 cm
  2. 25 cm
  3. 35 cm
  4. 50 cm

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A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners

Mensuration

A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is

  1. 8960
  2. 5120
  3. 4830
  4. 6420

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A right circular cone, a right circular cylinder and a hemisphere, all have the same radius

Mensuration

A right circular cone, a right circular cylinder and a hemisphere, all have the same radius, and the heights of cone and cylinder equal their diameters. Then their volumes are proportional, respectively to

  1. 2 : 1 : 3
  2. 3 : 2 : 1
  3. 1 : 2 : 3
  4. 1 : 3 : 1

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A slab of ice 8 inches in length, 11 inches in breadth, and 2 inches thick was melted

Mensuration

A slab of ice 8 inches in length, 11 inches in breadth, and 2 inches thick was melted and re-solidified into the form of a rod of 8 inches diameter. The length of such a rod, in inches, is nearest to

  1. 3
  2. 3.5
  3. 3
  4. 4.5

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A right circular cone of height h is cut by a plane parallel to the base and at a distance h/3

Mensuration

A right circular cone of height h is cut by a plane parallel to the base and at a distance h/3 from the base, then the volumes of the resulting cone and the frustum are in the ratio

  1. 1 : 4
  2. 1 : 7
  3. 8 : 19
  4. 1 : 3

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In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length

Mensuration

In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length of the longer side. What is the ratio of the shorter to the longer side?

  1. 2 : 5
  2. √3 : 2
  3. 3 : 4
  4. 1 : √3

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Four horses are tethered at four corners of a square plot of side 14 m

Mensuration

Four horses are tethered at four corners of a square plot of side 14 m so that the adjacent horses can just reach one another. There is a small circular pond of area 20 m2 at the centre. Find the ungrazed area.

  1. 168 m2
  2. 84 m2
  3. 42 m2
  4. 22 m2

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From a circular sheet of paper with a radius 20 cm, four circles of radius 5 cm each are cut out

Mensuration

From a circular sheet of paper with a radius 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion?

  1. 4 : 3
  2. 4 : 1
  3. 3 : 1
  4. 1 : 3

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In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively

Mensuration

In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?

  1. 17.05
  2. 22.45
  3. 26.25
  4. 27.85

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If a right circular cylinder of height 14 is inscribed in a sphere of radius 8

Mensuration

If a right circular cylinder of height 14 is inscribed in a sphere of radius 8, then the volume of the cylinder is

  1. 110
  2. 220
  3. 440
  4. 660

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