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Directions: Each of the questions below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer.
1
Car A is moving behind car B in the same direction and the distance between them initially is 40 km and the speed of car B is 50 km/hr, then how long would car A take to cross car B. [Assume the length of the cars to be negligible]
 
Statement I : The time taken car B to cover a distance of 200 km is 4 hours.
 
Statement II : if the cars were moving in the opposite directions, towards each other, the relative speed of car A with respect to car B would have been 120 km/hr.
» Explain it
B
Statement I :

We can calculate the speed of car B by this statement but the speed of car B is already given in the question.

Therefore, statement I alone is not sufficient to answer the question

Statement II :

Speed of car B = 50 km/hr

Distance between car A and car B = 40 km

Relative speed = 120 km/hr

Speed of car A = 120 – 50 = 70 km/hr

Required time taken by car A to cross car B

40  = 2 hours
70 – 50

Therefore, statement II alone is sufficient to answer the question

So, the data in Statement II alone is sufficient to answer the question, while the data in Statement I alone is not sufficient to answer the question.

Hence, option B is correct.
2
A man rows a boat upstream for a certain distance at a speed of 18 km/hr. If the ratio of speed of man in still water to the speed of stream is 5 : 2, find the time taken to row a boat downstream to cover the same distance covered upstream.
 
Statement I : The total time taken by the man to cover upstream and downstream is 25/7 hours.
 
Statement II : The time taken to cover the distance upstream is 2.5 hours.
» Explain it
C
Statement I :

Let the speed of man in still water be 5x and speed of stream be 2x

Upstream speed = 18 km/hr

So, 5x – 2x = 18

3x = 18

x = 6 km/hr

Downstream speed = 5x + 2x = 7x = 7 x 6 = 42 km/hr

Let the distance covered upstream be x km

So, the distance covered downstream be x km

So,  x  +  x  = 3  4
18 42 7

x = 45 km

Time taken to row a boat downstream to cover the same distance covered upstream

45  = 1.07 hours
42

Therefore, statement I alone is sufficient to answer the question

Statement II :

Let the speed of man in still water be 5x and the speed of stream be 2x

Upstream speed = 18 km/hr

So, 5x – 2x = 18

3x = 18; x = 6 km/hr

Downstream speed = 5x + 2x = 7x = 7 × 6 = 42 km/hr

Distance covered upstream = 18 × 2.5 = 45 km

Time taken to row a boat downstream to cover the same distance covered upstream

45  = 1.07 hours
42

Therefore, statement II alone is sufficient to answer the question

So, the data either in Statement I or in Statement II alone are sufficient to answer the question.

Hence, option C is correct.
3
Vivek mixes water and milk in an empty container A. Find the amount of water mixed by Vivek. 
 
Statement I : The ratio of the amount of water and the amount of milk in the container A is 5 : 13, respectively after Vivek has mixed milk and water. Vivek sells 72 litres of the mixture and then adds 44 more litres of a mixture of water and milk in the container. After mixing 44 more litres of the mixture, the ratio of the amount of water and the amount of milk becomes 4 : 9, respectively. 
 
Statement II : The ratio of the amount of water and the amount of milk in the container A is 5 : 13, respectively after Vivek has mixed milk and water. Vivek sells 72 litres of the mixture and then adds 44 more litres of a mixture of water and milk in the container in the ratio 5 : 6, respectively. 
» Explain it
D
Statement I :

Let, the amount of water and the amount of milk initially in the container = 5x litres and 13x litres, respectively

Amount of water sold by Vivek =  5  × 72 = 20 litres
18

Amount of milk sold by Vivek =  13  × 72 = 52 llitres
18

Since the amount of water and the amount of milk in 44 litres of the mixture which has been mixed later is not given

Therefore, statement I alone is not sufficient to answer the question

Statement II :

Let, the amount of water and the amount of milk initially in the container = 5x litres and 13x litres, respectively

Amount of water sold by Vivek =  5  × 72 = 20 litres
18

Amount of milk sold by Vivek =  13  × 72 = 52 llitres
18

Amount of water in 44 litres of mixture =  5  × 44 = 20 litres
11

Amount of milk in 44 litres of mixture =  6  × 44 = 24 litres
11

But the amount of mixture after mixing 44 litres of another mixture is not given

Therefore, statement II alone is not sufficient to answer the question

Combining statement I and statement II :

Let, the amount of water and the amount of milk initially in the container = 5x litres and 13x litres, respectively

And, the amount of water and the amount of milk after mixing 44 litres of mixture = 4y litres and 9y litres, respectively

Amount of water sold by Vivek =  5  × 72 = 20 litres
18

Amount of milk sold by Vivek =  13  × 72 = 52 llitres
18

Amount of water in 44 litres of mixture =  5  × 44 = 20 litres
11

Amount of milk in 44 litres of mixture =  6  × 44 = 24 litres
11

So, 5x – 20 + 20 = 4y
 
5x = 4y; y =  5x
4

And, 13x – 52 + 24 = 9y

13x – 28 = 9 ×  5x
4

52x – 112 = 45y

7x = 112; x = 16

The amount of water mixed by Vivek = 5x = 80 litres

So, the data in both statements I and II together are necessary to answer the question

Hence, option D is correct.
4
Water and alcohol have been added in an empty container. Find the amount of water that has been added in the container. 
 
Statement I : The ratio in which water and alcohol have been added is 11 : 5, respectively and 160 litres of the mixture has been sold after mixing. Then 25 litres of water and 25 litres of alcohol are mixed in the container and the ratio of water and alcohol became 2 : 1, respectively.
 
Statement II : The ratio in which water and alcohol have been added is 11 : 5, respectively. If 80 litres of another mixture of water and alcohol has been added then the ratio of water and alcohol became 5 : 3, respectively.
» Explain it
A
Statement I :

Let, amount of water and alcohol mixed initially in the container be 11x and 5x, respectively

So,  11x – 110 + 25  =  2
5x – 50 + 25 1

11x – 85 = 10x – 50

x = 35

Therefore, amount of water initially added in the container = 11 × 35 = 385 litres

Therefore, statement I alone is sufficient to answer the question

Statement II :

Let, amount of water and alcohol mixed initially in the container be 11x and 5x, respectively

Since, the ratio of water and alcohol in another mixture has not been given

Therefore, statement II alone is not sufficient to answer the question

So, the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question

Hence, option A is correct.
5
There is a cylindrical tank in a society in which water is stored. What is the height of the tank?
 
Statement I : The time taken to fill the tank through a pipe at a rate of 112 m3 of water per minute is 22 minutes. The cost of painting the curved surface area of the tank at Rs. 4 per m2 is Rs. 2816. 
 
Statement II : The curved surface area of the tank is 704 m2 and the time taken by a pipe to empty the tank is 28 minutes. 
» Explain it
A
Statement I:

Volume of the tank = 112 × 22 = 2464 m3

πr2 h = 2464 m3

Curved surface area of the tank =  2816  = 704 m2
4

2πrh = 704 m2

So,  πr2 h  =  2464
2πrh 704

r  = 3.5
2

r = 7

Since 2 πrh = 704

h =  204 × 7  = 16 m
2 × 22 × 7

Therefore, statement I alone is sufficient to answer the question

Statement II:

Curved surface area of the tank = 704 m2

2πrh = 704 m2

Since the rate at which the pipe is emptying the tank is not given

Therefore, we cannot find the height of the tank using the above information

Therefore, statement II alone is not sufficient to answer the question

So, the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question

Hence, option A is correct.