Quants 16 - Ratio and Proportion

Practice Questions:

Question 1:

The students in three batches at Mindworkzz are in the ratio 2 : 3 : 5. If 20 students are increased in each batch, the ratio changes to 4 : 5 : 7. The total number of students in the three batches before the increases were

2x + 20 : 3x + 20 : 5x + 20 = 4 : 5 : 7 Æ x = 10 and initially the number of students would be 20, 30 and 50 Æ a total of 100.

Question 2:

The speeds of three cars are in the ratio 2 : 3 : 4. The ratio between the times taken by these cars to travel the same distance is

The ratio of time would be such that speed × time would be constant for all three. Thus if you take the speeds as 2x, 3x and 4x respectively, the times would be 6y, 4y and 3y respectively. (LCM of 2, 3, 4 is 12 and so (2 x 6; 3 x 4; 4 x 3).

Question 3:

` 2250 is divided among three friends Amar, Bijoy and Chandra in such a way that 1/6th of Amar’s share, 1/4th of Bijoy’s share and 2/5th of Chandra’s share are equal. Find Amar’s share.

(a) ` 720 

(b) ` 1080

(c) ` 450 

(d) ` 1240

Amar’s share should be divisible by 6. Option d gets rejected by this logic.

Further: A + B + C = 2250. If Amar’s share is 720 (acc. To option a) Bijoy’s share should be 480 & Chandra’s share should be 300. (Gives us a total of 720 + 480 + 300 = 1500).

But the required total is 2250 (50% more than 1500). Since all relationships are linear, 1500 will increase to 2250 if we increase all values by 50%. Hence, Amar’s share should be 1080.

Question 4:

If 30 oxen can plough 1/7th of a field in 2 days, how many days 18 oxen will take to do the remaining work?

60 oxen days = 1/7 of the field Æ 420 oxen days are required to plough the field. Thus, the remaining work would be 360 oxen days. With 18 oxen, it would take 20 days.

Question 5:

A cat takes 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speed of the cat to that of the dog?

Assume that 1 cat leap is equal to 3 metres and 1 dog leap is equal to 4 metres.
Then the speed of the cat in one unit time = 3 × 5 = 15 meters.
Also, the speed of the dog in one unit time = 4 × 4 = 16 meters.
The required ratio is 15:16

Time to Think:

If 30 men working 7 hours a day can do a piece of work in 18 days, in how many days will 21 men working 8 hours a day do the same work?