CAT Questions

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

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

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

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

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 From the second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in two-thirds the time.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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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?

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?

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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Mensuration

Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is

  1. 3√2
  2. 3
  3. 4
  4. √3

Mensuration

The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar is

  1. 1300
  2. 1340
  3. 1480
  4. 1520

Geometry

A circle is inscribed in a given square and another circle is circumscribed about the square. What is the ratio of the area of the inscribed circle to that of the circumscribed circle?

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

Geometry

A semicircle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn meeting the circumference of the semi-circle at D. Given that AC = 2 cm and CD = 6 cm, the area of the semicircle (in sq. cm) will be:

  1. 32 π
  2. 40.5 π
  3. 50 π
  4. 81 π

Geometry

Consider obtuse angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer then how many such triangles exist?

  1. 5
  2. 10
  3. 15
  4. 21

Geometry

If in the figure below, angle XYZ = 90° and the length of the arc XZ = 10π, then the area of the sector XYZ is

  1. 10π
  2. 25π
  3. 100π
  4. None of the above

Geometry

AB is a chord of a circle. The length of AB is 24 cm. P is the midpoint of AB. Perpendiculars from P on either side of the chord meets the circle at M and N respectively. If PM < PN and PM = 8 cm. then what will be the length of PN?

  1. 17 cm
  2. 18 cm
  3. 19 cm
  4. 20 cm
  5. 21 cm

Geometry

AB, CD and EF are three parallel lines, in that order. Let d1 and d2 be the distances from CD to AB and EF respectively. d1 and d2 are integers, where d1 : d2 = 2 : 1. P is a point on AB, Q and S are points on CD and R is a point on EF. If the area of the quadrilateral PQRS is 30 square units, what is the value of QR when value of SR is the least?

  1. slightly less than 10 units
  2. 10 units
  3. slightly greater than 10 units
  4. slightly less than 20 units
  5. slightly greater than 20 units