Quant question with Answers 2

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Quant question with Answers

1. A leopard spots a deer from a distance of 200 meters. As the leopard starts chasing the deer, the deer also starts running. Given that the speed of the deer is 10 km/h and that of the leopard is 12 km/h, how far would have the deer run before it is caught?


A. 3 km
B. 4 km
C. 2 km
D. 1 km
E. 5 km

2. Paul, Quallis and Robert divide a sum of money among themselves in the ratio 2:3:7. Find the share of Paul if the total share of Paul and Quallis together is $1500 less than that of Robert.

A. 2000
B. 1200
C. 1400
D. 2500
E. 1500

4. The length of rectangle ABCD is 6/5th of its breadth. Its perimeter is 132. Find its area.

A. 660 m²
B. 2210 m²
C. 1080 m²
D. 2160 m²
E. 460 m²

3. Find the speed of a man in still water if he goes upstream at 6 km/h when the rate of stream is 2 km/h.

A. 2 km/h
B. 8 km/h
C. 6 km/h
D. 14 km/h
E. 4 km/h

5. The prices of a TV and a refrigerator are in the ratio 9:5. If the TV costs $4,200 more than the refrigerator does, what is the price of the refrigerator?

A. 4200
B. 5400
C. 6000
D. 5250
E. 4600

6. 40% of the people of a certain locality suffer from Diabetes, 25% suffer from Leprosy and 10% suffer from both. What percentage of the people do not suffer from either of the diseases?

A. 30%
B. 35%
C. 40%
D. 45%
E. 50%

7. A bag contains balls, marbles and tops. The triple ratio of balls to marbles to tops in the bag is 20 : 4 : 6. If there are 120 balls in the bag, find the number of tops in the bag.

A. 66
B. 36
C. 26
D. 49
E. 12

8. The cost of a camera at 20% discount is $100. Find its actual price.

A. $125
B. $130
C. $225
D. $335
E. $105

9. It takes 16 days for 48 women to complete a job that requires 16 men to complete in 24 days. 12 men initiated the work and after 14 days, 12 women joined them. How many days will they together take to complete the job?

A. 12
B. 21
C. 6
D. 24
E. 16

10. Where does p lie if p² < p?

A. Between -1 and 0
B. Between -1 and 1
C. Between 0 and 1
D. It is always less than 0
E. It is always greater than 1

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1. Correct Answer: D

Solution:
The relative speed can be given as 12 - 10 = 2 km/h. So the leopard will catch the deer after 0.2/2 = 1/10 hour.
Hence the distance covered by the deer before it is caught can be calculated as 10 * 1/10 = 1 km. Hence 4.

2. Correct Answer: E
Solution:
Let the total amount of money they have be T
And the respective shares of Paul, Quallis and Robert be P, Q and R.
Now, P + Q + R = T ----- (1) and given that the amount is to be divided in the ratio of 2 : 3 : 7, the total share of P and Q is $1500 less than R, i.e.,
P + Q = R - 1500 ----- (2)
From (1) and (2);
P + Q = T - R ----- (3)
Comparing equation (2) and (3)
R - 1500 = T - R;
2 R = 1500 + T; or
R = (1500 + T) / 2 ----- (4)
But R's share is
[7 / (2 + 3 + 7)] * T = (7/12) T ----- (5)
From (4) and (5),
(1500 + T) / 2 = (7/12) T
18000 = 14 T - 12 T
T = 9000.
So total amount is $ 9000.
P's share = [2 / (2 + 3 + 7)] * 900 = $1500.
Hence 5.

4) Correct Answer: C
Solution:
Let x be the length and y be the breadth of the given rectangle.
Now, given that,
x = 6/5 y -------- (1)
and
2 x + 2 y = 132 -------- (2)
Substituting x in (2) by results in (1), we get,
2 (6/5 y) + 2 y = 132; or 12/5 y + 2 y = 132. Multiplying both sides by 5, we get,
12 y + 10 y = 660;
22 y = 660
y = 30.
Since x = 6/5 y, x = 6/5 * 30 = 36. Therefore, area = x * y = 36 * 30 = 1080 m².
Hence 3.

5) Correct Answer: D
Solution:
Let the cost of TV be x.
So, the cost of refrigerator will be x - 4200.
Given, the ratio of the cost of the TV and refrigerator is 9 : 5 Therefore,
cost of TV / cost of refrigerator = 9 / 5
or, x / (x - 4200) = 9 / 5
5 x = 9 (x - 4200)
4 x = 4200 * 9
x = 9450.
So, the cost of refrigerator is x - 4200 = 5250.
Hence 4.

3) Correct Answer: B
Solution:
Speed in still water can be calculated as the actual speed upstream + the rate or speed of stream
= 6 + 2
= 8 km/h.
Hence 2.

7) Correct Answer: B
Solution:
Let the total number of items (balls, marbles and tops) in the bag be x.
Given that the ratio of balls to marbles to tops is 20 : 4 : 6.
Number of balls = 120.
Now, Number of balls = [20 / (20 + 4 + 6)] * x
Or, x = 120 * (30/20) = 180
Total number of items = 180
Number of tops = (6/30) * 180 = 36.
Hence 2.

8) Correct Answer: A
Solution:
Let the actual price of the camera be $x.
x - 0.2 x = 100; or
0.8 x = 100; or
x = $125.
Hence 1

9) Correct Answer: A
Solution:
Total work = Number of men * Number of days = Number of women * Number of days.
Or, 16 men * 24 days = 48 women * 16 days.
Therefore, 48 women = (16 * 24) / 16 = 24 men;
or 1 man is as efficient as 2 women are.------(1).
Now, 12 men work for 14 days. The remaining work, (16 * 24) - (12 * 14) = 216 man-day.
Since 12 women, that are equivalent to 6 men join the 12 men, effective strength = 12 + 6 = 18 men. Number of days to complete remaining 216 man-days of work = 216 / 18 = 12 days.
Hence 1.

6) Correct Answer: D
Solution:
Percentage of people suffering from Diabetes = 40.
Percentage of people suffering from Leprosy = 25.
Percentage of people suffering from both, Diabetes and Leprosy = 10.
The percentage of people suffering from either Diabetes or Leprosy = 40 + 25 - 10 = 65 - 10 = 55.
Total percentage of people in the locality = 100.
Hence the percentage of people suffering from neither of the diseases = 100 - 55 = 45.
Hence 4.

10) Correct Answer: C
Solution:
Given that p² < p.
The first option is incorrect because if p lies between -1 and 0, p² will never be less than p.
Statement 2 is also incorrect because for certain values of p (between - 1 and 1), the value of p² may or may not be less than p. For example, if we take p = (- 0.6), the value of p² > p; whereas if we take p = 0 or 0.6, then the value of p² = p or p² < p.
According to option 3, p > 0 but less than 1. This is the only range in which for every value of p, the value of p² is always less than p.
Hence option 3 is the correct one.