## Fourth 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 fourth 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 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.

### 4th WBCS Main level Arithmetic solution set: time to answer 10 mins

#### Problem 1

In a river a man takes 3 hrs in rowing 3kms upstream, but rowing downstream he covers 15kms in same 3 hrs. The speed of the river current is,

- 2km/hr
- 4km/hr
- 9km/hr
- 6km/hr

#### Problem 2

The product of two successive positive integers is 1980. The smaller of the number is,

- 34
- 44
- 45
- 35

#### Problem 3

A shop owner gains the selling price of 20 chairs by selling 100 chairs. What is his gain percent?

- 15%
- 12%
- 25%
- 20%

#### Problem 4

The rational numbers lying between $\displaystyle\frac{1}{4}$ and $\displaystyle\frac{3}{4}$ are,

- $\displaystyle\frac{262}{1000}$, $\displaystyle\frac{752}{1000}$
- $\displaystyle\frac{9}{40}$, $\displaystyle\frac{31}{41}$
- $\displaystyle\frac{13}{50}$, $\displaystyle\frac{264}{350}$
- $\displaystyle\frac{63}{250}$, $\displaystyle\frac{187}{250}$

#### Problem 5

The ratio of two numbers is 5 : 8 and their difference is 69. The numbers are,

- 69, 128
- 115, 184
- 128, 197
- 43, 112

#### Problem 6

By what least number must 21600 be multiplied to make it a perfect cube?

- 10
- 30
- 6
- 60

#### Problem 7

The value of $\left[\left\{\left(-\displaystyle\frac{1}{2}\right)^2\right\}^{-2}\right]^{-1}$ is,

- $\displaystyle\frac{1}{4}$
- $\displaystyle\frac{1}{16}$
- $4$
- $16$

#### Problem 8

Each side of a rhombus is 5cm. Its area is,

- 23 cm sq
- 24 cm sq
- 25 cm sq
- data insufficient

#### Problem 9

If $A:B=\displaystyle\frac{1}{6} : \displaystyle\frac{1}{5}$, $B:C=\displaystyle\frac{1}{4} : \displaystyle\frac{1}{3}$, and $C:D=\displaystyle\frac{1}{3} : \displaystyle\frac{1}{5}$, then $A:D$ is,

- $\displaystyle\frac{1}{24} : \displaystyle\frac{1}{25}$
- $\displaystyle\frac{1}{25} : \displaystyle\frac{1}{29}$
- $\displaystyle\frac{1}{24} : \displaystyle\frac{1}{29}$
- $\displaystyle\frac{1}{27} : \displaystyle\frac{1}{25}$

#### Problem 10

3 men or 5 women can do a work in 12 days. In how many days will 6 men and 5 women will take to complete the work?

- 4 days
- 15 days
- 20 days
- 10 days

### Related detailed solution set

Refer to the companion * WBCS Main level solution set 4* for detailed explanation of the concepts and quick methods of solution.

### Answers to the questions

**Problem 1. ****Answer:** Option a: 2km/hr.

**Problem 2. ****Answer:** Option b: 44.

**Problem 3.** **Answer:** Option c: 25%.

**Problem 4.** **Answer:** Option d: $\displaystyle\frac{63}{250}$, $\displaystyle\frac{187}{250}$.

**Problem 5.** **Answer:** Option b: 115, 184.

**Problem 6.** **Answer:** Option a: 10.

**Problem 7.** **Answer:** Option: b: $\displaystyle\frac{1}{16}$.

**Problem 8.** **Answer:** Option d: data insufficient.

**Problem 9.** **Answer:** Option a: $\displaystyle\frac{1}{24} : \displaystyle\frac{1}{25}$.

**Problem 10.** **Answer:** Option: a: 4 days.

### Important tutorials on Arithmetic topics

**Numbers, Number systems and basic arithmetic operations**

**Fractions and decimals basic concepts part 1**

**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 6**

**WBCS Main level Arithmetic Question set 6**

**WBCS Main level Arithmetic Solution set 5**

**WBCS Main level Arithmetic Question set 5**

**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**