# IAS Exam: IAS Prelims CSAT Basic Numeracy Set 1

For the Civil Services aspirants, here, we have provided numerical test paper for the IAS Prelim Examination.

In the Civil Services Prelim Examination, the CSAT paper has been made qualifying in nature from 2015 onwards. The candidates have to score at least qualifying marks in the paper but in case, if a candidate could not be able to score the required qualifying marks in CSAT Paper then his/her other papers will not be evaluated. So, it is important for the candidates to do preparation in such a manner that there must not lay them in any suspicion of underscoring.

**Category: Ratio and proportion**

1. The income of A, B and C are in the ratio 7: 9: 12 and their expenditure are in the ratio 8 : 9 : 15. If a saves 1/4 of his income. Find the ratio of savings of A, B and C.

a) 56 : 99 : 69

b) 69 : 56 : 99

c) 99 : 56 : 69

d) 99 : 69 : 56

Answer (a)

Explanation:

Let income of A, B and C are and and their expenditure are 8y, 9y and 15y respectively.

According to question

**Category: Averages**

2. In a team, the average weight was found to be 'x' kg. After deducting computational error, the average weight of 94 candidates got reduced from 84 to 64. The average thus came down by 18.8 kgs. The numbers of candidates who were in the team are:

a) 100

b) 90

c) 110

d) 105

Answer (a)

Explanation:

3. A family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 65 years, that of the parents is 40 years and that of the grandchildren is 12 years. What is the average age of the family?

a) 28 4/7 years

b) 31 5/7 years

c) 32 1/7 years

d) 35 1/7 years

Answer (d)

Explanation:

Total no. of people = 2 + 2 + 3 = 7

Average age of grand-parents = 65

Total age of grand-parents = 65 × 2 = 130

Similarly, Total age of parents = 2 × 40 = 80

Total age of grand children = 12 × 3 = 36

Combined Total age = 130 + 80 + 36= 246

**Category: Speed and distance**

4. Two cities X and Y are 450 km apart. A car travels from X to Y with a speed of 80 km/hr and returns to X with a speed of 120 km/hr. What is the average speed of the car?

a) 95 km/hr

b) 96 km/hr

c) 100 km/hr

d) 110 km/hr

Answer (b)

Explanation:

**Category: Permutation and combination**

5. In a college reunion, friends of the same sex to hug and for friends of opposite sex to shake hands when they meet. During the reunion there were 24 handshakes. Which one among the following numbers indicates the possible number of hugs?

a) 39

b) 30

c) 21

d) 20

Answer (c)

Explanation:

Let x be no. of women and y be no. of men.

Then no. of handshakes = x*y = 24.

Then factors of 24 are (6, 4); (8, 3); (12, 2).

Thus x or y = 6 and y or x = 4, it is immaterial for present answer.

Then start placing the 3 groups of factors. We find that for first, number of hugs is 21; for second 68; for third 31.

Only 21 is given in answer

6. A selection is to be made for one post of Manager and two posts of Assistant manager. Amongst the six candidates called for the interview, only two are eligible for the post of Manager while they all are eligible for the post of Assistant manager. The number of possible combinations of selectees is

a) 4

b) 12

c) 18

d) None of the above

Answer (d)

Explanation:

Only two candidates are eligible for the post of Manager

The Manager can be selected in 2 ways. All candidates are eligible for the post of Assistant manager.

Any two of the remaining five candidates after the Manager is selected can be selected as the Assistant manager.

The first Assistant manager can be selected in five ways.

The second Assistant manager can be selected out of the remaining four in four ways.

7. A student has to opt for 2 activities out of 5 activities for extra curriculum, namely, singing, Drama, dancing, Sports and horse riding. Horse riding can be offered only if Sports is also opted. The number of different combinations of two activities which can be opted is

a) 5

b) 6

c) 7

d) 8

Answer (C)

Explanation:

If Horse riding is not opted for, then two activities out of four activities have to be opted for.

If Horse riding is opted for, then it can be offered only if Sports is also opted for. Number of ways in which two subjects can be opted for = 6+1 = 7.

**Category: Number system**

8. An auto-manufacturing company has three machines producing the same auto part. If machine A produces 1/6th as many of the item as machine B produces in the same time and machine B produces twice as many of the item as machine C in the same time, then during a fixed period machine C produces what fraction of the total number of items produced?

a) 2/15

b) 3/10

c) 7/17

d) 7/15

Answer: b)

Explanation:

Assuming, Machine A produces 100 units in a certain time period.

Machine B would produce 6 times of X or 600 units.

Machine C would produce half of that = 300 units

The three machines together would produce 1000 units, of which 300 are produced by machine C.

9. Find out the days in which a man and a woman together can complete the piece of work, if 3 men alone and 4 women alone can complete a piece of work in 5 days?

a) 60/7 days

b) 7 days

c) 9 days

d) Cannot be determined

Answer (a)

Explanation:

3 men can complete a work in 5 days

1 man can complete a work in 3 × 5 days= 15 days

4 women can complete a work in 4 days

1 woman can complete a work in 4 × 5 days= 20 days

10. A group of men decided to do a job in 10 days. But since 20 men dropped out every day, the job completed at the end of the 14^{th} day. How many men were there at the beginning?

a) 240

b) 345

c) 455

d) 560

Answer(c)

Explanation:

Let n be the initial number of worker then

10n = n + (n – 20) + (n – 40) + … + (n – 260)

10n = 14n – 1820

4n = 1820

n = 455 workers

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