# Maths Data Sufficiency Questions PDF with Solution for Bank, Insurance and CET Exam

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
Pranav and Pankaj started working together. After a few days, Prashant joined them and they were able to finish the work in 10 days. All of them together were paid a total of Rs. 800. Find the share of Prashant.

Statement I : Pranav can do the work in 20 days, while Pankaj can do the same work in 25 days.

Statement II : Pranav can do the work in 60 days, while Pankaj can do the same work in 15 days.
» Explain it
C
From statement I:

In 1 day, Pranav finishes 1/20th of the work.

In 1 day, Pankaj finishes 1/25th of the work.

The work was completed in 10 days.

Part of work completed by Pranav and Pankaj in 10 days

 = 10 ( 1 + 1 ) = 9 20 25 10

 Part of work completed by Prashant = 1 – 9 = 1 10 10

Amount received as payment will be proportional to the amount of work done.

 Amount paid to Prashant = 800 × 1 = Rs. 80 10

Similarly, from statement II we also can find the share of Prashant.

∴ Either of the statements alone is sufficient to answer this question.

Hence, option C is correct.
2
Two partners, P and Q entered in a business, what profit will Q get at the end of 2 years?

Statement I : P and Q started the business by investing in the ratio 4: 7 and After 2 years, P’s share is Rs. 95000.

Statement II : P joined the business with an amount of Rs. 500000
» Explain it
A
From statement I:

Share of profit of P and Q will be in the ratio of 4 : 7

After two years,

Let the share of profit of Q be Rs. y

 ∴ 4 = 95000 7 y

 ⇒ y = 95000 × 7 4

⇒ y = Rs. 166250

∴ Statement I alone is sufficient to answer.

From statement II: Only P's investment is given so we can't find the profit of Q.

Hence, option A is correct.
3
Find the number of boys in the college, if 60% of the total boys and 40% of  the total girls participated in an event.

Statement I : The number of girls participated in the event is 120. There are more than 300 boys in the college.

Statement II : The number of girls in the college is 25% more than the number of boys who participated in the event.
» Explain it
D
From Statements I and II:

40% of girls participated in the event, which is equals to 120

 ∴ 100% ⇒ 120 × 100 = 300 40

∴ Total number of girls in the college = 300

The number of boys who participated in the event
 ⇒ 300 × 100 = 240 125

Total number of boys participated is 240, which is equals to 60%

 ∴ 100% ⇒ 240 × 100 = 400 60

∴ Total number of boys in the college = 400

∴ Statement I and II together are necessary to answer the questions.

Hence, option D is correct.
4
Find the total population of Kanpur.

Statement I : The ratio of the population of males and females in Kanpur is 33 : 29 and the difference between their population is 24000.

Statement II : The population of Kanpur is 60% of that of Patna, and the difference between population of Kanpur and Patna is 35000.
» Explain it
C
From statement I:

Let the total population of Kanpur be X.

⇒ 32X – 29X = 24000

⇒ 4X = 24000

⇒ X = 6000

∴ The total population 33X + 29X = 62X

62X = 62 × 6000 = 372000

From statement II:

Let the total population of Kanpur be X.

 So, population of Patna = 100X = 5X 60 3

 ∴ 5X – X = 35000 3

⇒ 2X = 105000

⇒ X = 52500

∴ Statement I or II alone is sufficient to answer the question.

Hence, option C is correct.
5
Find the speeds of trains A and B, if running in the same direction the faster train passes the slower in 54 seconds. The speed of train A is more than train B.

Statement I : Trains A and B of lengths 140 metres and 130 metres respectively are running on parallel tracks.

Statement II : When running in opposite directions, they pass each other in 24 seconds.
» Explain it
D
Let the speed of trains A and B be x and y respectively

From statements I:

Total distance = 140 + 130 = 270 metres

Relative speed = (x – y)

 ∵ Speed = Distance Time

 ∴ (x – y) = 270 ..........(i) 54

From statement II:

Relative speed = x + y

 ⇒ x + y = 270 ...........(ii) 24

By using equations (i) and (ii), we can calculate the value of x and y

∴ Both the statements are required to answer this question.

Hence, option D is correct.