## Sixth 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 sixth question set on Arithmetic, 10 specially selected questions are included. You should answer this question set first before referring to its companion solution set. Link of the solution set is available at the end.

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**

### 6th WBCS Main level Arithmetic question set: time to answer 10 mins

#### Problem 1

If the ratio of three numbers are $3:4:5$ and their LCM is 1200, then the smallest number is,

- 80
- 60
- 120
- 100

#### Problem 2

The least number which when diminished by 5 is divisible by each of 21, 28, 36, 45 is,

- 425
- 1260
- 1265
- 1259

#### Problem 3

A container contains $x$ litres of milk. $y$ litres of milk was taken out and replaced by water. How much milk will be there in the container after carrying out this process $(n-1)$ times?

- $x\left(1-\displaystyle\frac{y}{x}\right)^n$ litres
- $x\left(1-\displaystyle\frac{y}{x}\right)^2$ litres
- $x\left(1-\displaystyle\frac{y}{x}\right)^{n-1}$ litres
- $x\left(1-\displaystyle\frac{y}{x}\right)^3$ litres

#### Problem 4

What number should come next in the sequence, 6, 18, 72, 360, 2160...?

- 15120
- 12120
- 13120
- 14120

#### Problem 5

A pump can fill a tank with water in 2 hrs. Because of a leak developed in the tank, it takes now $2\displaystyle\frac{1}{2}$ hrs to fill the tank. The leak will empty the full tank with pump not running, in,

- $8$ hrs
- $10$ hrs
- $14$ hrs
- $2\displaystyle\frac{1}{3}$ hrs

#### Problem 6

Gold is 19 times as heavy as water and copper is 9 times as heavy as water. The ratio in which these two metals are to be mixed so that the mixed alloy becomes 15 times as heavy as water is,

- 2 : 3
- 1 : 2
- 3 : 2
- 19 : 135

#### Problem 7

A student was asked to divide a number by 3, but instead of dividing he multiplied it by 3 and got 29.7 as the result. The correct answer would be,

- 9.9
- 9.3
- 9.8
- 3.3

#### Problem 8

Which of the following fractions is the largest?

- $\displaystyle\frac{7}{8}$
- $\displaystyle\frac{63}{80}$
- $\displaystyle\frac{31}{40}$
- $\displaystyle\frac{13}{16}$

#### Problem 9

A fisherman can row 2 km against the stream in 20 minutes and return in 15 minutes. The speed of the boat in still water is,

- $2$ km per hour
- $3$ km per hour
- $1\displaystyle\frac{1}{2}$ km per hour
- $7$ km per hour

#### Problem 10

Two trains running in opposite direction cross a man standing on the platform in 27 secs and 17 secs respectively and they cross each other in 23 secs. The ratio of their speeds is,

- 1 : 3
- 3 : 2
- 2 : 3
- 3 : 4

### Related detailed solution set

Refer to the companion * WBCS Mains level solution set 6* for detailed explanation of the concepts and quick methods of solution.

### Answers to questions

**Problem 1.** Answer: Option b: 60.

**Problem 2.** Answer: Option c: 1265.

**Problem 3.** Answer: Option c: $x\left(1-\displaystyle\frac{y}{x}\right)^{n-1}$ litres.

**Problem 4.** Answer: Option a: 15120.

**Problem 5.** Answer: Option b: 10 hrs.

**Problem 6.** Answer: Option c: 3 : 2.

**Problem 7.** Answer: Option d: 3.3.

**Problem 8.** Answer: Option a: $\displaystyle\frac{7}{8}$.

**Problem 9.** Answer: Option d: $7$ km per hour.

**Problem 10.** Answer: Option b: 3 : 2.

### Question and Solution sets on WBCS Main Aritmetic

**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**