MAT PO CAT

Quantitative Aptitude

Sample Paper 3

Question 1. A rectangular tank is 225 m by 162 m at the base. With what speed must water flow into it through an aperture 60 cm by 45 cm that the level may be raised 20 cm in 5 hours?

  1. 5000 m/hr
  2. 5400 m/hr
  3. 5200 m/hr
  4. 5600 m/hr

Answer: Volume of water added in 5 hours `= 225 xx 162 xx 0.2 = 7290` cubic m
Now, length covered by water through aperture in 5 hours = Volume/Area
`= (7290)/(0.6 xx 0.45) = 27000` m
Flow in 1 hour `= (27000)/5 = 5400` m per hour
Hence, option B is the right answer.

Question 2. At a point on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is 5/12. On walking 192 metres towards the tower, the tangent of the angle of elevation is 3/4.The height of the tower is:

  1. 160 m
  2. 180 m
  3. 170 m
  4. 190 m

Answer: In Δ ABC; tan θ `= (AB)/(AC)`
Or, `5/(12) = (AB)/(AC)`
Or, `AB = `(5AC)/(12)` …… (1)

In Δ ABD; tan θ `= (AB)/(AD)`
Or, `3/4 = (AB)/(AD)`
Or, `AB = (3AD)/4` ……… (2)

From equations (1) and (2);
`(5AC)/(12) = (3AD)/4`
Or, `5AC = 9AD`
Or, `5(AD + 192) = 9AD`
Or, `5AD + 960 = 9AD`
Or, `4AD = 960`
Or, `AD = (960)/4 = 240`

Using this value of AD; we can calculate the height as follows:
`AB = (3AD)/4`
`= 3 xx (240)/4 = 180` m
So, option B is the right answer.


Question 3. A school has 4 sections of chemistry in Class X having 40, 35, 45 and 42 students. The mean marks obtained in Chemistry test are 50, 60, 55 and 45 respectively for the 4 sections. Determine the overall average of marks per student.

  1. 50.25
  2. 52.25
  3. 51.25
  4. 53.25

Answer: Average `= (40 xx 50 + 35 xx 60 + 45 xx 55 + 42 xx 45)/(40 + 35 + 45 + 42)`
`= (2000 + 2100 + 2475 + 1890)/(162) = (8465)/(162) = 52.25`
Option B is the correct answer.

Question 4. The average score of boys in an examination of a school is 71 and that of girls is 73.The average score of the school in that examination is 71.8.Find the ratio of the number of boys to the number of girls that appeared in the examination.

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

Answer: If number of boys is B and that of girls is G then; `(71B + 73G)/(B + G) = 71.8`
Or, `71B + 73G = 71.8B + 71.8G`
Or, `0.8B = 1.2G`
Or, `B/G = (1.2)/(0.8) = 3:2`
Option C is the correct answer.


Question 5. Company C sells a line of 25 products with an average retail price of Rs.1, 200. If none of these products sells for less than Rs 420 and exactly 10 of the products sell for less than Rs.1, 000, what is the greatest possible selling price of the most expensive products?

  1. Rs.2, 600
  2. Rs.7, 800
  3. Rs.3, 900
  4. Rs.11, 800

Answer: Let us assume that 10 products sell for Rs. 420 each.
Then price of these 10 products = 4200
Total price of 25 products `= 25 xx 1200 = 30000`
Total price of remaining 15 products `30000 – 4200 = 25800`
If remaining 14 products sell for Rs. 1000 each
Then total price of 14 products = 14000
So, price of last product `= 30000 – (4200 + 14000) = 30000 – 18200 = 11800`
Option D is the correct answer.

Question 6. A sink contains exactly 12 litres of water. If water is drained from the sink until it holds exactly 6 litres of water less than the quantity drained away, how many litres of water were drained away?

  1. 2
  2. 6
  3. 3
  4. 9

Answer: Let us solve this question by using option D, i.e. 9
If 9 litre water is drained then remaining water in the sink = 12 – 9 = 3 litre
Difference = 9 – 3 = 6 litre
So, option D is the correct answer.


Question 7. A chemist has 10 litres of a solution that is 10 per cent nitric acid by volume. He wants to dilute the solution to 4 per cent strength by adding water. How many liters of water must be added?

  1. 15
  2. 20
  3. 18
  4. 25

Answer: 10% of 10 litre = 1 litre
So, amount of water = 9 litre
If 1 litre is 4% then total volume `= (100)/4 = 25` litre
So, amount of water = 24 litre
So, additional amount of water = 24 – 9 = 15 litre
Option A is the correct answer.

Question 8. A company received two shipments of ball bearings. In the first shipment,1 per cent of the ball bearings were defective. In the second shipment, which was twice as large as the first, 4.5 per cent of the ball bearings were defective. If the company received a total of 100 defective ball bearings, how many ball bearings were there in the first shipment?

  1. 990
  2. 2,000
  3. 1,000
  4. 3,000

Answer: Since quantity in second shipment is 2 times that in first shipment
Hence, 4.5% of second shipment = 9% of first shipment
Percentage of defective ball bearing to 1st shipment = 9 + 1 = 10%
Since 10% of 1st shipment = 100
So, total quantity in 1st shipment `= 100 xx 10 = 1000`
Option C is the correct answer.


Question 9. Population of a district is 2, 96,000 out of which1, 66,000 are male.50% of the population is literate. If 70% male are literate, the number of women who are literate, is?

  1. 32,200
  2. 31,800
  3. 66,400
  4. 48,000

Answer: Number of literate persons = 50% of 296000 = 148000
Number of literate male = 70% of 166000 = 116200
So, number of literate women = 148000 – 116200 = 31800
Option B is the correct answer.

Question 10. A train covers 180 km distance in 4 hours. Another train covers the same distance in 1 hour less. What is the difference covered by these trains in one hour?

  1. 45km
  2. 9km
  3. 40 km
  4. None of these

Answer: Speed of first train `= (180)/4 = 45` km/h
Speed of second train `= (180)/3 = 60` km/h
Difference `= 60 – 45 = 15` km
Option D is the correct answer.