 IAS Exam: IAS Prelims CSAT Basic Numeracy Set 3

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 cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1: 3: 4:5. When the pieces were sold, the merchant got Rs. 98,000 less. Find the original price of the diamond?

a) Rs. 1.4lakh
b) Rs. 2 lakh
c) Rs. 1 lakh
d) Rs. 2.1 lakh

Explanation:

As Cost of the diamond =kW2 [K is proportionality constant]
So, 100kW2 - (1+9+16+25) kW2 = 98,000
=>kW2 = 2000
Price of the diamond = 2000 x 100 = 2lakh.

Category: Averages

2.The average age of S and G is 35 years. If K replaces S, the average age becomes 32 years and if K replaces G, then the average age becomes 38 years. If the average age of D and I be half of the average age of S, G and K, then the average age of all the five people is:

a) 28 years
b) 32 years
c) 25 years
d) None of these

Explanation: 3.The average monthly salary of 24 executives and 3 HR professionals in a company was Rs. 6000. When one of the HR professional whose salary was Rs. 7200, was replaced with a new manager, then the average salary of the team went down to 5900. What is the salary of the new HR professional?

a) 1800
b) 2400
c) 3800
d) 4200

Explanation:

Let the salary of the new HR professional be X
(30 *6000)−7200 + x = 5900 * 30
X = 4200

Category: Speed and distance

4. It takes 16 hours for a 1200 km journey, if 240 km is done by train and the rest by car. It takes 40 minutes more, if 400 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is?

a) 2: 3
b) 3: 2
c) 3 : 4
d) 4 : 3

Explanation:

Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 240/x + 960/y = 16        .... (i)
And, 400/x + 800/y  = 50/3  .... (ii)
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 3: 4.

Category: Permutation and combination

5.In how many ways can four boys be made to stand in a line such that two of them, Ram and Shyam are always together?

a) 6
b) 12
c) 18
d) 24

Explanation: If the boys are Ram , Shyam, A, B we have to consider Ram & Shyam as    one boy. This, would give us 3! ways of arranging Ram shyam, A and B. However, for every arrangement with Ram shyam, there would be a parallel arrangement with Shyam Ram. Thus, the    correct answer would be 3! × 2! = 12 ways.

6. In the given figure, what is the maximum number of different ways in which 8 identical marbles can be placed in the small triangles A, B, C and D such that each triangle contains at least one marble? a) 32
b) 35
c) 44
d) 56

Explanation: The ways of placing the marbles would be 5, 1, 1, 1 (4!/3! = 4 ways); 4, 2, 1 & 1 (4!/2! = 12 ways); 3, 3, 1, 1 (4!/2! × 2! = 6 ways); 3, 2, 2, 1 (4!/2! = 12 ways) and 2, 2, 2, 2 (1 way). Total number of ways = 4 + 12 + 6 + 12 + 1 = 35 ways.

7. Two teams played a mixed doubles badminton game (each team consists of one male and one female). There are four married couples. No team is to consist of a husband and his wife. What is the maximum number of games that can be played?

a) 12
b) 21
c) 36
d) 42

Explanation:  First select the two men. This can be done in   ways. Let us say the men are A, B, C and D and their respective wives are  a, b, c and d.

If we select A and B as the two men then while selecting the women there would be two cases as seen below: Hence, the required answer is 18 + 24 = 42 ways. Hence, option (d) is correct.

Category: Number system

8.6 friends P, Q, R, S, T and U went for an appraisal meeting. After the appraisal the salary of Q was 20% more than P; salary of R was 30% less than Q; salary of S was 40% more than R; salary of T was 50% less than S and the salary of U was 60% more than T. If all the friends had the same salary before the appraisal, then which is the correct order of appraisal?

a) U > T > S > R > Q > P
b) Q > S > P > U > R > T
c) S > Q > U > P > R > T
d) T > Q > S > P > U > R

Explanation:
After appraisal their salaries are:
P = x
Q = 1.2x
R = 0.84x
S = 1.1176
T = .588x
U = .9408x

9. Pipe A can fill an empty tank in 10 minutes, while another pipe, B, can empty the same full tank in 6 minutes. If both the pipes are open and the tank is already 2/5th full, how long will it take to empty or fill the tank completely?

a) 6 min. to fill
b) 6 min. to empty
c) 9 min. to empty
d) 9 min. to fill

Explanation: When A & B are opened together, they will empty the tank. 10.A vendor bought some bananas at 4 per rupee and an equal number at 5 per rupee. When he sold the entire quantity at 9 for 2 rupees. What is his percentage profit or loss?

a) No profit, no loss
b) 8.88% profit
c) 6.66% loss
d) 1.23% loss