## Third 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 third question set on Arithmetic, 10 representative questions are included. The time recommended is 10 minutes.

Before going through the test, to *refresh concepts* on any topic or to know *how to solve problems at a high speed*, you should refer to **our concept tutorials and articles** listed below.

### Concept tutorials and articles on Arithmetic

#### Number system, fractions and surds

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

**Factorization or finding out factors**

**Fractions and decimals, basic concepts part 1**

**How to solve surds part 1 rationalization**

**How to solve surds part 2 double square root surds and surd term factoring**

**How to find perfect square root of integers or decimals New**

#### Ratio and proportion and mixing liquids

**Arithmetic problems on mixing liquids and based ages**

**How to solve arithmetic mixture problems in a few steps 1**

**How to solve arithmetic mixture problems in a few steps 2**

#### Percentage

**Basic and rich percentage concepts**

#### Componendo dividendo

**Componendo dividendo explained**

#### Simple interest and compound interest

**Basic and rich concepts on simple interest and compound interest**

#### Work time, work wages and pipes and cisterns

**How to solve arithmetic problems on work time, work wages and pipes and cisterns**

**How to solve time work problems in simpler steps type 1**

**How to solve time work problems in simpler steps type 2**

#### Speed time distance, train problems and boats in rivers

**Basic concepts on speed time distance, train running and boats and rivers**

**How to solve time distance problems in a few simple steps 1**

**How to solve time distance problems in a few simple steps 2**

#### Profit and loss

**How to solve in a few steps profit and loss problems 1**

**How to solve similar problems in a few seconds profit and loss problems 2**

**How to solve difficult profit and loss problems in a few steps 3**

**How to solve difficult profit and loss problems in a few steps 4**

#### Clocks and Calendars

**How to solve Clock problems New**

**How to solve Calendar problems New**

### 3rd WBCS main level Arithmetic: time 10 mins

#### Problem 1

The simplified value of $\displaystyle\frac{1}{56}+\displaystyle\frac{1}{72}+\displaystyle\frac{1}{90}+\displaystyle\frac{1}{110}+\displaystyle\frac{1}{132}$ would be,

- $\displaystyle\frac{5}{84}$
- $\displaystyle\frac{1}{12}$
- $\displaystyle\frac{1}{84}$
- $\displaystyle\frac{1}{28}$

#### Problem 2

A man cultivates $\displaystyle\frac{1}{3}$rd of a land in 10 days while a second man cultivates $\displaystyle\frac{2}{5}$th of the same land in 6 days. In how many days would the two cultivate $\displaystyle\frac{4}{5}$th of this land if they work together?

- 4 days
- 10 days
- 5 days
- 8 days

#### Problem 3

The value of $(0.\overline{1})^2\left[1-9\times{(0.1\overline{6})^2}\right]$ is,

- $-\displaystyle\frac{1}{162}$
- $\displaystyle\frac{1}{109}$
- $\displaystyle\frac{1}{108}$
- $\displaystyle\frac{7696}{10^6}$

Problem 4

The least number of square tiles required to pave the floor of a room 15m 17cm long and 9m 2cm broad is,

- 814
- 902
- 738
- 656

#### Problem 5

If $2A=3B=4C$, then $A : B : C$ is,

- 4 : 3 : 2
- 6 : 4 : 3
- 2 : 3 : 4
- 3 : 4 : 5

#### Problem 6

By selling an item for Rs.350 instead of Rs.400, the percentage loss increases by 5%. The cost price of the item is,

- Rs.1050
- Rs.1000
- Rs.433
- Rs.417.50

#### Problem 7

The average of the first 100 natural numbers is,

- 50.5
- 51
- 50
- 51.5

#### Problem 8

The bell of a wall-clock requires 3 seconds to ring 5 times. The time required for the bell to ring 6 times is,

- $3\displaystyle\frac{1}{2}$ seconds
- $4$ seconds
- $5$ seconds
- $3\displaystyle\frac{3}{4}$ seconds

#### Problem 9

Two numbers are in the ratio of 3 : 5. If each number is increased by 10, the ratio becomes 5 : 7. The numbers are,

- 3, 5
- 7, 9
- 15, 25
- 13, 22

#### Problem 10

The area of a square is equal to the area of a circle. The ratio between a side of the square and the radius of the circle is,

- $1 : \sqrt{\pi}$
- $\sqrt{\pi}:1$
- $\pi : 1$
- $1:\pi$

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

* WBCS Main level Arithmetic solution set 3*.

### Answers to the questions

**Problem 1. ****Answer:** Option a: $\displaystyle\frac{5}{84}$.

**Problem 2. ****Answer:** Option d: 8 days.

**Problem 3.** **Answer:** Option c: $\displaystyle\frac{1}{108}$.

**Problem 4.** **Answer:** Option a: 814.

**Problem 5.** **Answer:** Option b: 6 : 4 : 3.

**Problem 6.** **Answer:** Option b: Rs.1000.

**Problem 7.** **Answer:** Option: a: 50.5.

**Problem 8.** **Answer:** Option d: $3\displaystyle\frac{3}{4}$ seconds.

**Problem 9.** **Answer:** Option c: 15, 25.

**Problem 10.** **Answer:** Option: b: $\sqrt{\pi}:1$.

### Question and Solution sets on WBCS Main Arithmetic

**WBCS main level Arithmetic Solution set 11**

**WBCS main level Arithmetic Question set 11**

**WBCS main level Arithmetic Solution set 10**

**WBCS main level Arithmetic Question set 10**

**WBCS main level Arithmetic Solution set 9**

**WBCS main level Arithmetic Question set 9**

**WBCS main level Arithmetic Solution set 8**

**WBCS main level Arithmetic Question set 8**

**WBCS Main level Arithmetic Solution Set 7**

**WBCS Main level Arithmetic Question Set 7**

**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**