MAT PO CAT

# Quantitative Aptitude

## Sample Paper 4

Question 1. Speed of a speed –boat when moving in the direction perpendicular to the direction of the current is 16 km/hr, speed of the current is 3 km/hr. So the speed of the boat against the current will be (km/hr)?

- 22
- 9.5
- 10
- None of these

**Answer:** Speed of boat `= 16 – 3 = 13` km/h

Speed of boat against the current `= 13 – 3 = 10` km/h

Option C is the correct answer.

Question 2. R and S start walking towards each other at 10 A.M. at speed of 3 km/hr and 4km/hr respectively. They were initially 17.5 km apart. At what time do they meet?

- 2:30P.M.
- 11:30P.M.
- 1:30P.M.
- 12:30P.M.

**Answer:** Relative speed of R and S `= 3 + 4 = 7` km/h

Time to cover 17.5 km `= (17.5)/7 = 2.5` hours

So, they will meet at 12:30 PM

Option D is the correct answer.

Question 3. A shopkeeper marks up his goods to gain 35%.But he allows 10% discount for cash payment .His profit on the cash transaction therefore, in percentage, is:

- 13.5
- 25
- 21.5
- 31.5

**Answer:** 10% of 135 = 13.5

So, selling price `= 135 – 13.5 = 121.5`

So, percentage profit `= 121.5 – 100 = 21.5%`

Option C is the right answer.

Question 4. A can do 50% more as B can do in the same time .B alone can do a piece of work in 20 hours. A, with the help of B can finish the same work in how many hours?

- 12
- 8
- 13.5
- 5.5

**Answer:** Since A can do 50% more than what B can do in the same time so, A will take 33.3% less time to finish the work.

Time taken by A = 20 – 33.3% of 20 `= 20 – (20)/3 = (40)/3`

Work done in 1 hour when both A and B work together `= 1/(20) + 3/(40) = (2 + 3)/(40) = 5/(40) = 1/8`

So, time taken when both work together = 8 hour

Option B is the correct answer.

Question 5. Profits of a business are distributed among three partners A, B and C in such a way that 4 times the amount received by A is equal to 6 times the amount received by B and 11 times the amount received by C. The ratio in which the three received the amount is:

- 4:6:11
- 11:6:4
- (1/4) : (1/6) : (1/11)
- 66:44:24

**Answer:** Let us use option C to solve this question.

`4xx1/4 = 1`

`6xx1/6 = 1`

`11xx1/(11) = 1`

It satisfies the conditions given in question.

So, option C is the correct answer.

Question 6. A train covered a certain distance at uniform speed. If the train had been 6 km/h faster it would have taken 4 hours less than the scheduled time. And, if the train were slower by 6 km/h. the train would have taken 6 hours more than the scheduled time. The length of the journey is:

- 700 km
- 740 km
- 720 km
- 760 km

**Answer:** Difference between speeds = 6 + 6 = 12 km/h

Difference between timings = 4 + 6 = 10 hours

Only one option, i.e. C is divisible by both 12 and 10

Let us solve by using this option

If speed = 12 km/h then time `= (720)/(12) = 60` hour

If speed = 24 km/h then time `= (720)/(24) = 30` hour

If speed = 36 km/h then time `= (720)/(36) = 20` hour

Difference in timings at speeds 24 km/h and 36 km/h = 10 hour

So, option C is the correct answer.

Question 7. Students of a class are made to stand in rows. If 4 students are extra in each row, there would be 2 rows less. If 4 students are less in each row, there would be 4 more rows. The number of students in the class is:

- 90
- 94
- 92
- 96

**Answer:** If number of rows = x and number of students in each row = y

So, total number of students `= xy`

If 4 students are extra in each row then total number of students can be given by `(x – 2)(y + 4)`

Of 4 students are less in each row then total number of students can be given by `(x + 4)(y – 4)`

Or, `(x – 2)(y + 4) = xy`

Or, `xy + 4x – 2y – 8 = xy`

Or, `4x – 2y – 8 = 0`

Similarly, `(x + 4)(y – 4) = xy`

Or, `xy – 4x + 4y – 16 = xy`

Or, `4x – 4y + 16 = 0`

Or, `4x – 2y – 8 – 4x + 4y – 16 = 0`

Or, `2y – 24 = 0`

Or, `2y = 24`

Or, `y = 12`

Only one option, i.e. D is divisible by 12.

So, D is the right answer.

You can cross check your answer as follows:

96/12 = 8

96/8 = 12 (4 extra rows)

96/16 = 6 (2 less rows)

Question 8. A part of monthly expenses of a family is constant and the remaining varies with the price of wheat. When the rate of wheat is Rs.250 a quintal, the total monthly expenses of the family are Rs.1000 and when it is Rs.240 a quintal, the total monthly expenses are Rs.980.Find the total monthly expenses of the family when the cost of wheat is Rs.350 a quintal.

- Rs.1000
- Rs.1400
- Rs.1200
- Rs.800

**Answer:** When rate of wheat decreases by Rs. 10 per quintal, the monthly expenses decreases by Rs. 20.

So, rate of wheat increases by Rs. 100 per quintal, the monthly expenses will increase by Rs. 200

Hence, increased expenses = Rs. 1200

Option C is the right answer.

Question 9. A plane left 30 minutes later than the scheduled time and in order to reach the destination 1500 km away in time, it had to increase the speed by 250 km/h from the usual speed. Find its usual speed:

- 720 km/h
- 740 km/h
- 730 km/h
- 750 km/h

**Answer:** Let us solve this question by using option D because only this option can divide 1500 km

If speed is 750 km/h then time `= (1500)/(750) = 2` hour

If speed is 750 + 250 = 1000 km/h then time `= (1500)/(1000) = 1.5` hour

Difference in time = ½ hour = 30 minute

So, option D is the correct answer.

Question 10. A metallic sheet is of rectangular shape with dimensions 48 cm x 36 cm. From each one of its corners, a square of 8 cm is cut off. An open box is made of the remaining sheet. Find the volume of the box.

- 5110 cm
^{3} - 5130 cm
^{3} - 5120 cm
^{3} - 5140 cm
^{3}

**Answer:** Length = 48 – 16 = 32 cm, width = 36 – 16 = 20 cm and height = 8 cm

So, volume `= 32 xx 20 xx 8 = 5120` cm^{3}

Option C is the right answer.