## Sample Aptitude Questions

**1.Two trains 130 and 110 meters long are going in the same direction. The faster train takes one minute to pass the other completely. If they are moving in opposite directions, they pass each other completely in 3 seconds. Find the speed of the faster train.**

A.38 m/sec

B.46 m/sec

C.42 m/sec

D.50 m/sec

**Answer & Explanation**

**Answer: Option C**

Total Distance to be travelled by both the trains

= 130 + 110 = 240m

Let ‘F ’and ‘S’ be the speeds of fast and slow trains in m/sec. 240=60(F-S), 240= (F+S)

In the same direction , F – S = 4 m/sec ……(1)

In the opposite direction , F + S =80 m/sec……(2)

Solving them we get F = 42 m/sec.

**2.A motor boat can travel at 10 km/h in still water. It travelled 91 km downstream in a river and then returned, taking altogether 20 hours. Find the rate of flow of the river.**

A.6 km/hr

B.5 km/hr

C.8 km/hr

D.3 km/hr

**Answer & Explanation**

**Answer: Option D**

Given, speed of the Boat in still water (B)=10 km/hr

Let S be the speed of flow of river, then

91/(10+S) + 91/(10-S) = 20, Then going by options

91/13 – 91/7 = 20

So, S = 3 km/hr.

**3.The total tractor population in a state is 2,94,000, out of which 1,50,000 are made by Mahindra & Mahindra. Out of every 1,000 Mahindra tractors, 98 are red in colour, but only 5.3% of the total tractor population is red. Find the percentage of non-Mahindra tractors that are red.**

A.0.5025%

B.0.5130%

C.0.6125%

D.0.6140%

**Answer & Explanation**

**Answer: Option C**

Total tractor population = 2,94,000

Mahindra & Mahindra = 1,50,000

So, Non Mahindra trucks = 1,44,000

Since out of every 1000 Mahindra tractors, 98 are red, out of 1,50,000 Mahindra tractors 14,700 are red.

5.3% of 2,94,000 = 15,582 are red tractors in all.

So non Mahindra tractors which are red

=15,582 – 14,700 = 882

Hence percentage of non Mahindra tractors that are red = 882/144,000 * 100 = 0.6125%

**4.7% of the total quantity of wheat is lost in grinding when a country has to import 12 million tonnes, but when only 51⁄5 is lost, it can import 3 million tonnes. Find the quantity of wheat grown in the country.**

A.500 million tonnes

B.400 million tonnes

C.600 million tonnes

D.700 million tonnes

**Answer & Explanation**

**Answer: Option A**

Difference in % of wheat lost = 7 – 26/5 = 9/5%

Difference in import = 12 – 3 = 9 million As 9/5% % of total qty of wheat = 9 million

⇒ 9x/500 = 9

⇒ x = 500 million

**5.A man who can swim 48 m/min in still water swims 200 m against the current and 200 m with the current. If the difference between those 2 times is 10 minutes, find the speed of the current.**

A.30 m/min

B.29 m/min

C.31 m/min

D.32 m/min

**Answer & Explanation**

**Answer: Option D**

Try option & get answer as fourth option:

(200/(48 – 32)) – (200/ (48 + 32)) (12(1/2)min – 2(1/2)min)

= 10 min

**6.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.

**7.Mira’s expenditure and saving are in the ratio 3:2. Her income increases by 10%. Her expenditure also increases by 12%. By how much % do her saving increase?**

A.7%

B.9%

C.10%

D.13%

**Answer & Explanation**

**Answer: Option A**

Let total income be = 5

Increased income will be = 5.5

Increased expenditure will be = 3.36

Increased saving will be = 5.5 – 3.36 = 2.14

Percentage increase will be = 14/2 * 100 = 7%

**8.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.

**9.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

**10.The length of a rectangular field is double its width, inside the field there is a square-shaped pond 8 m long. If the area of the pond is 1/8 of the field, what is the length of the field?**

A.32 m

B.16 m

C.64 m

D.20 m

**Answer & Explanation**

**Answer: Option A**

Area of Pond = 64

Area of field = 64 × 8 = 512

Area of field ⇒ x . 2x = 512

⇒ 2×2 = 512 ⇒ x2 = 256 ⇒ x = 16

Length = 2 × 16 = 32. So A option is answer.