WBCS Main level Arithmetic Question set 2

Second question set for WBCS Main level Arithmetic


Compulsory paper VI of WBCS Main is on Arithmetic and Test of Reasoning. It has 200 questions to be answered in 180 minutes. In this second question set on Arithmetic, 10 representative questions are included. The time recommended is 10 minutes.

How to prepare before you answer the question set

To prepare for Arithmetic, you need to build the base of Arithmetic concepts step by step on: Number system, Factorization, HCF and LCM, Fractions surds and decimals, Indices, Ratio and Proportion, Average and Percentage. You may learn concepts from corresponding Tutorials in this website, and NCERT books.

Together with concept reading, you have to practice solving a lot of sums on these base topics from NCERT books or good online resources. Unless you give enough dedicated time on this phase of building the base, you will fall short in next steps.

After building the base, preparation should start on the Applications of Arithmetic—topics on Time and Work, Work and wages, Speed time distance, Boats in rivers, Profit and loss, Simple interest and Compound interest, Mixture or Alligation, and so on.

Following same method, you should do concept reading and then problem solving on each topic. Worked out sums from NCERT books, and concept tutorials from this website should quickly give you confidence to start solving problems yourself.

Important to remember—One: Understand concepts first

Without understanding worked out sums or going through concept reading you shouldn't start to practice solving sums.

Important to remember—two: Ability in maths builds step by step

Don't skip any step. For example, without giving sufficient time on say, visualization of factors in multiples, or building Arithmetic base, you should not try to conquer Arithmetic applications.

Important to remember—three: Don't be impatient with maths preparation

Compared to any other subject in competitive exams, building Maths excellence takes maximum time. Be patient, work systematically and hard in a planned manner.

After you covered these three, the last and most important item confronts you.

In competitive math MCQ tests, you can't think of solving sums procedurally step by step, you must practice solving such problems in mind, wholly based on concepts, but in mind applying analytical reasoning. With as little writing as possible. This is what we call Efficient Math Problem solving.

After answering this question set, scoring yourself (+2 correct, -0.5 incorrect) and measuring time, if you go through the companion solution (link given at the end), you might get an idea on what we mean by efficient math problem solving.

Now let us get down to solving the question set with your time watch on.

2nd WBCS main level Arithmetic: time 10 mins

Problem 1

If sum of two numbers is 10 and the sum of their reciprocals is $\displaystyle\frac{5}{12}$, the numbers would be,

  1. 6 and 4
  2. 8 and 2
  3. 9 and 1
  4. 7 and 3

Problem 2

A man bought 4 trousers at Rs.750 each, 4 shirts at Rs.450 each and 12 pairs of shoes at Rs.750 each. What is the average expenditure per item?

  1. Rs.900
  2. Rs.1000
  3. Rs.690
  4. Rs.800

Problem 3

A dishonest dealer declares that he sells his goods at cost price, but actually he uses a false weight of 900gms for 1kg weight. His profit percentage is,

  1. $13%$
  2. $11.25%$
  3. $12\displaystyle\frac{1}{9}%$
  4. $11\displaystyle\frac{1}{9}%$

Problem 4

Which of $\sqrt[3]{3}$ and $\sqrt{2}$ is larger?

  1. $\sqrt[3]{3}$
  2. $\sqrt{2}$
  3. The two are equal
  4. None of the above

Problem 5

If P is 50% of Q and Q is 50% of R then, P : Q : R is,

  1. 4 : 2 : 1
  2. 1 : 2 : 4
  3. 2 : 1 : 4
  4. 1 : 4 : 2

Problem 6

The number of digits of the square root of 0.00059049 is,

  1. 6
  2. 5
  3. 3
  4. 4

Problem 7

What is the ratio of areas of two squares if the ratio of their diagonals is 5 : 2?

  1. 125 : 8
  2. 5 : 2
  3. 4 : 25
  4. 25 : 4

Problem 8

Two trains, each 100m long and moving in opposite directions, cross each other in 8 secs. If one is moving twice as fast as the other, the speed of the faster train is,

  1. 60km/hr
  2. 70km/hr
  3. 50km/hr
  4. 40km/hr

Problem 9

In what ratio must water be mixed with milk to make a profit of $16\displaystyle\frac{2}{3}$% on selling the diluted milk at cost price?

  1. 6 : 1
  2. 4 : 3
  3. 2 : 3
  4. 1 : 6

Problem 10

A policeman, while running to catch a thief, is 114m behind the thief. The policeman runs 21m and the thief runs 15m every minute. In what time will the policeman catch the thief?

  1. 18 minutes
  2. 16 minutes
  3. 19 minutes
  4. 17 minutes

Solutions to these problems with conceptual explanation, and how to solve the problems easily and quickly, are available in companion solution set,

WBCS Mains level Arithmetic solution set 2.

Answers to the questions

Problem 1. Answer: Option a: 6 and 4.

Problem 2. Answer: Option c: Rs.690.

Problem 3. Answer: Option d: $11\displaystyle\frac{1}{9}$.

Problem 4. Answer: Option a: $\sqrt[3]{3}$.

Problem 5. Answer: Option b: 1 : 2 : 4.

Problem 6. Answer: Option d: 4.

Problem 7. Answer: Option d: $\displaystyle\frac{25}{4}$.

Problem 8. Answer: Option a: 60km/hr.

Problem 9. Answer: Option d: 1 : 6.

Problem 10. Answer: Option c: 19 minutes.

Important tutorials on Arithmetic topics

Numbers, Number systems and basic arithmetic operations



Fractions and decimals basic concepts part 1

Ratio and proportion

Arithmetic problems on mixing liquids and based on ages

How to solve Arithmetic problems on Work time, Work wages and Pipes and cisterns

Basic concepts on problems on speed time distance, Train running and Boats in rivers

Basic and rich concepts on Simple interest and Compound interest

Basic and rich percentage concepts

Question and Solution sets on WBCS Main Aritmetic

WBCS Main level Arithmetic Solution set 4

WBCS Main level Arithmetic Question set 4

WBCS Main level Arithmetic Solution set 3

WBCS Main level Arithmetic Question set 3

WBCS Main level Arithmetic Solution set 2

WBCS Main level Arithmetic Question set 2

WBCS Main level Arithmetic Solution set 1

WBCS Main level Arithmetic Question set 1