CAT 2020: Ratio & Proportion | Additional Study Material for CAT PDF Download

Q.1. A sum of money is split among Amal, Sunil and Mita so that the ratio of the shares of Amal and Sunil is 3:2, while the ratio of the shares of Sunil and Mita is 4:5. If the difference between the largest and the smallest of these three shares is Rs 400, then Sunil’s share, in rupees, is

Ans: 800
Given ratio of shares of Amal and Sunil is 3: 2
Also the ratio of shares of Sunil and Mita is 4: 5.
Hence the ratio of shares of Anil, Sunil and Mita is 6: 4: 5
∴ Sunil's share = 400 x 4 / 2 = 800

Q.2. The distance from B to C is thrice that from A to B. Two trains travel from A to C via B. The speed of train 2 is double that of train 1 while traveling from A to B and their speeds are interchanged while traveling from B to C. The ratio of the time taken by train 1 to that taken by train 2 in travelling from A to C is
(a) 1 : 4
(b) 7 : 5
(c) 5 : 7
(d) 4 : 1

Correct Option is C
Given,

Let the speed of train 1 from A to B be s.
Then the speed of train 2 from A to B is 2s.
Time taken by train 1 to cover A to C =
And, time taken by train 2 to cover A to C
=
Required ratio =

Q.3. A and B are two points on a straight line. Ram runs from A to B while Rahim runs from B to A. After crossing each other, Ram and Rahim reach their destinations in one minute and four minutes, respectively. If they start at the same time, then the ratio of Ram's speed to Rahim's speed is
(a) 2
(b) √2
(c) 2√2
(d) 1/2

Correct Option is A
Required ratio of speeds = Square root of inverse ratio of times taken after crossing each other.
= √4 : √1 i.e., 2: 1

Q.4.  John takes twice as much time as Jack to finish a job. Jack and Jim together take onethirds of the time to finish the job than John takes working alone. Moreover, in order to finish the job, John takes three days more than that taken by three of them working together. In how many days will Jim finish the job working alone? 

Ans: 4
Let the individual times taken by John, Jack and Jim to complete the works be a, b and c respectively.
Given, a = 2b....... (1)


From (1) and (2), we've c = 2b
∴
⇒ b = 2
∴ c = 4

Q.5. A contractor agreed to construct a 6 km road in 200 days. He employed 140 persons for the work. After 60 days, he realized that only 1.5 km road has been completed. How many additional people would he need to employ in order to finish the work exactly on time?

Ans: 40

X = 140 x 4.5/1.5 x 60/140 = 180
Additional men required = 180 - 140 = 40