Directions: Each of the questions below consists of a question and two statements numbered I, and II 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.
Important for :
1
How many students from IIT Dhanbad got the placement?

Statement I : Number of students studying in IIT Dhanbad and IIT Kanpur are in the ratio of 3 : 4 respectively and 80% of the students studying in IIT Kanpur got placement.

Statement II : Number of students who got placement from IIT Kanpur is 120% of the number of students who got placement from IIT Dhanbad.
» Explain it
E
From statement I :

Let, no. of students studying in IIT Dhanbad and IIT Kanpur are 3x and 4x respectively.

No. of students studying in IIT Kanpur who got placement

 = 4x × 80 = 16x 100 5

From statement II :

No. of students studying in IIT Kanpur who got placement = 120% of No. of students studying in IIT Dhanbad who got placement hence,

 ⇒ 16x = 120% of y 5

 ⇒ y = 8x 3

∴ Question cannot be answered even with the information in both the statements.

Hence, option E is correct.
2
Virat’s income is how much more than Rohit’s income?

Statement I : Virat’s income is 30% less than his wife, whose provident fund deduction is Rs. 975 per month which is 5% of her monthly income.

Statement II : Rohit spends 30% of his income on house rent, 15% of which is accessory bill and Virat’s expenditure on house rent is Rs. 4500 more than that of Rohit’s.
» Explain it
E
From statement I:

Let the income of Virat’s wife is Rs. x per month.

∴ According to the statement

⇒ 0.05x = 975

⇒ x = 19500/-

∴ Virat’s income is 70% of x

 = 19500 × 70 = Rs. 13650 100

Nothing is given about Rohit so we cannot find his income.

Rohit’s income can’t be calculated also from statement II.

Hence, option E is correct.
3
Two trains A and B are travelling towards each other on the same track. The initial distance between them is 91 km. Find the time, when the two trains will collide.

Statement I : The speed of train A is 65km/h and the speed of B is 104 km/h more than that of train A.

Statement II : The ratio of speeds of the two trains is 5 : 13.
» Explain it
A
Let distance travelled by slow train be x km. In time ‘t’,

From statement I :

Speed, 65 = distance/time = x/t

 ⇒ t = x ----(i) 65

for faster train, in same time ‘t’,

 Speed, 169 = distance = x time t

 ⇒ t = 91 – x ----(ii) 169

Equating (i & (ii),

 ⇒ x = 91 – x 65 169

⇒ 169x = 5915 – 65x

⇒ 234x = 5915

⇒ x = (5915/234)

Putting in (i),

 ⇒ t = x = 5915/234 = 5915 65 65 234 × 65

= 23.33 minutes.

Nothing can be conclusive using statement II,

∴ only statement I is sufficient.

Hence, option A is correct.
4
Find the amount of money invested by Jamnalal in the scheme?

Statement I : An increase in simple interest from 44/3% to 58/3% per annum increases his yearly income by 2800.

Statement II : The sum invested get doubled, when invested at 20% per annum for 5 years.
» Explain it
A
Let the invested amount be Rs. x

From statement I:

 ⇒ SI = P × r × n 100

 Increase in rate of interest = 58 – 44 = 14 % 3 3 3

Increase in SI because of increased rate of interest:

 ⇒ x × 14 × 1 3 100

This increase = Increase in income = 2800

 ⇒ x × 14 × 1 = 2800 3 100

 ⇒ x = 280000 × 3 = 60,000 14

From statement II :

⇒ SI = x

 ⇒ x = x × 20 × 5 100

From here x cannot be calculated

∴ Statement I alone is sufficient while statement II is not.

Hence, option A is correct.
5
Pipe A and B can fill a tank at the rate of 12 and 10 litre per minute respectively. There is a leakage also in the same tank. What is the capacity of the tank?

Statement I : If A and B are opened simultaneously, the tank is filled in 5 hours 45 minutes and a leakage hole drains the pipe at the rate of 6 litres/minute.

Statement II : Due to the leak the filled tank drains in 15 hours 20 minutes. If A and B are opened simultaneously, the tank is filled in 5 hours 45 minutes .
» Explain it
C
From statement I :

If both pipes and a leak operate simultaneously, then 12 + 10 – 6 = 16 litre per minute.

⇒ Capacity of the tank = 16 × (5 × 60 + 45) = 5520 litres

From statement II :

Let the leak drain out at the rate of x litre per minute. Then if both pipes and a leak operate simultaneously, 12 + 10 – x = 22 – x litres per minute.

⇒ Capacity of the tank = (22 – x) (5 × 60 + 45)

And again capacity of the tank = x (15 × 60 + 20)

Equal both above equations to obtain the value of x i.e. 6 litre per minute. Now put it any of the above equation to obtain the capacity of the tank.

∴ Either of two statements would be sufficient to obtain the solution.

Hence, option C is correct.