## 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.

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**

#### 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**

### 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,

- 6 and 4
- 8 and 2
- 9 and 1
- 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?

- Rs.900
- Rs.1000
- Rs.690
- 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,

- $13%$
- $11.25%$
- $12\displaystyle\frac{1}{9}%$
- $11\displaystyle\frac{1}{9}%$

#### Problem 4

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

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

#### Problem 5

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

- 4 : 2 : 1
- 1 : 2 : 4
- 2 : 1 : 4
- 1 : 4 : 2

#### Problem 6

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

- 6
- 5
- 3
- 4

#### Problem 7

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

- 125 : 8
- 5 : 2
- 4 : 25
- 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,

- 60km/hr
- 70km/hr
- 50km/hr
- 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?

- 6 : 1
- 4 : 3
- 2 : 3
- 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?

- 18 minutes
- 16 minutes
- 19 minutes
- 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.

### Question and Solution sets on WBCS Main Arithmetic

**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**