## Sample Aptitude Questions

**1.A garden is 24 m long and 14 m wide. There is a path 1 m wide outside the garden along its sides. If the oath is to be constructed with square marble tiles 20 cm × 20 cm, find the number of tiles required to cover the path.**

A.1800

B.2000

C.200

D.2150

**Answer & Explanation**

**Answer: Option B**

Area of field = 16 × 26 = 416 m2

Area of inner field = 24 × 14 = 336 m2

Remaining area = 416 – 336 = 80 m2

Area in cm = 80 × 100 × 100 = 800,000 cm2

Area of each marble = 20 × 20 = 400

No. of tiles = 800000/400 = 2000

**2.From the top of a cliff 25 m high, the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. Find the height of the tower.**

A.40 m

B.50 m

C.48 m

D.52 m

**Answer & Explanation**

**Answer: Option B**

ZP is parallel to XY, so angle ZPY = angle ZYX,

And angle PZY = angle QZP

Hence angle QZP = ZYX = PZY

As ZXY is 90, so the only possible value that satisfy the above angles is 45

Then XY = 25 m, PZ = 25 and PQ = 25

As x = 450, total height of tower will be

= 25 + 25 = 50 m

**3.A bath tub can be filled by a cold water pipe in 20 minutes and by a hot water pipe in 30 minutes. A person leaves the bathroom after turning on both pipes simultaneously and returns at the moment when the bath tub should be full. Finding however, that the waste pipe has been open, he now closes it. In 3 minutes more the bath tub is full. In what time would the waste pipe empty it?**

A.38 min

B.45 min

C.42 min

D.48 min

**Answer & Explanation**

**Answer: Option D**

Total work = 1/20 + 1/30

(3+2)/60 = 5/60 = 1/12

For both of them needed = 12 min.

But due to leakage it take = 15 min.

So we can say for filling pipe it takes 3 minutes

work for the waste pipe will be = 12 min.

3 min. of both filling pipe = 12 min. of waste pipe

12 min. of filling pipe will be = 48 min. of waste pipe i.e. our answer is 4th option

**4.A mixture of 45 liters of spirit and water contains 20% of water in it. How much water must be added to make the water 25% in the new mixture?**

A.5 litres

B.3 litres

C.4 litres

D.6 litres

**Answer & Explanation**

**Answer: Option B**

In Mixture | Spirit | Water |

36 | 9 |

On adding water in the mixture it becomes 25 % of mixture, so spirit will be 75 % of the mixture.

75% of Total = 36

⇒ Total = 36/0.75 = 48 liter. Hence 3 liter water is needed.

**5.In a year 28th February is Tuesday; if the leap year is excluded, then 28th March will be a**

A.Sunday

B.Tuesday

C.Monday

D.Saturday

**Answer & Explanation**

**Answer: Option B**

Simple counting of days.

28th Feb = Tuesday

28th March = Tuesday

**6.Ram’s age was square of a number last year and it will be cube of a number next year. How long must he wait before his age is again the cube of a number**

A.39 years

B.38 years

C.10 years

D.64 years

**Answer & Explanation**

**Answer: Option B**

First square then cube, this no will be after25, 27 years respectively. Next cube will be at 64 so he has to wait for 38 years.

**7.Two small circular parks of diameters 16 m, 12 m are to be replaced by a bigger circular park. What would be the radius of this new park, if the new park occupies the same space as the two small parks?**

A.10

B.20

C.15

D.25

**Answer & Explanation**

**Answer: Option A**

Some of areas of 2 smaller parks

= New bigger one

π(8)² + π(6)² = πr²

π[64+36] = πr²

π[100 = πr²

r= 10

**8.A bottle contains 3/4 of milk and the rest water. How much of the mixture must be taken away and replaced by equal quantity of water so that the mixture has half milk and half water?**

A.25%

B.33.33%

C.45%

D.50%

**Answer & Explanation**

**Answer: Option B**

Question can be solved by just putting value in Exp. Take total as 12 liter Quantity of milk & water will be 9, 3

Take out 1/3rd of mixture out now we have quantity of milk & water will be 6, 2

Now replace with water we get quantity of mixture will be 6, 6 liters. This is the required answer (2nd option) because we have replaced mixture with 4 liters of water.

**9.Two vessels contain spirit of 0.5 and 0.75 concentrations. If two liters from the first vessel and three liters from the second vessel are mixed, then what will be the ratio of the spirit and the water in the resultant solution?**

A.13 : 7

B.15 : 17

C.7 : 17

D.17 : 15

**Answer & Explanation**

**Answer: Option A**

Take 12, 12 liters in both mixtures which gives us

First

Spirit – 6

Water – 6

Second

Spirit – 9

Water – 3

Taking 2 liters from 1st mixture and 3 liters from 2nd mixture which gives us

First

Spirit – 1

Water – 1

Second

Spirit – 9/4

Water – 3/4

So total of sprit and water in new mixture will be =

Spirit | Water |

1 + (9/4) | 1 + (3/4) |

13/4 | 7/4 |

Which will give 1st option as the answer.

**10.A and B run a 5 km race on a round course of 400 m. if their speed be in the ratio 5 : 4, how often does the winner pass the other on circular track?**

A.4 times

B.3 times

C.5 times

D.2 times

**Answer & Explanation**

**Answer: Option D**

Total no. of round will be 5000/400 = 12.5 No. of rounds A completes to finish the race will be 12.5 and by the time B can complete only 10 rounds. (As ratio of speed of A & B is 5 : 4. So they meet for the first time after A has finished 5 rounds and B has finished 4 rounds.) So difference in no. of round will be = 21⁄2.

The winner meets the other 2 times because the winner meets the other after every 2000 meters.