## Ninth 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 ninth question set on Arithmetic, 10 selected questions of varied types are included.

The questions are followed by answers and link to the corresponding detailed solution set.

The solution set will provide valuable insight into how the problems can be solved quickly in mind followed by detailed explanation and concept elaboration when needed.

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**

### 9th WBCS Main level Arithmetic question set: time to answer: 10 mins

#### Problem 1

What will be the value of $8^{0.28}\times{4^{0.08}}$?

- $1$
- $4^{0.36}$
- $2$
- $8^{0.36}$

#### Problem 2

The selling price of an article is $\displaystyle\frac{4}{3}$ times its cost price. The gain percentage is,

- $33\displaystyle\frac{1}{3}$%
- $25\displaystyle\frac{1}{4}$%
- $20\displaystyle\frac{1}{2}$%
- $20\displaystyle\frac{1}{3}$%

#### Problem 3

In a mixture of 60 litres, the ratio of milk and water is 2 : 1. If the ratio of milk and water is to be 1: 2, then the amount of water (in litres) to be added is,

- 20
- 30
- 40
- 60

#### Problem 4

If $\text{20% of a} = \text{30% of b} = \displaystyle\frac{1}{6} \text{of c}$, then $a:b:c$ is,

- $2:3:16$
- $3:2:16$
- $10:15:18$
- $15:10:18$

#### Problem 5

Which fraction comes next in the sequence,

$\displaystyle\frac{1}{2}$, $\displaystyle\frac{3}{4}$, $\displaystyle\frac{5}{8}$, $\displaystyle\frac{7}{16}$,..?

- $\displaystyle\frac{12}{35}$
- $\displaystyle\frac{9}{32}$
- $\displaystyle\frac{11}{34}$
- $\displaystyle\frac{10}{17}$

#### Problem 6

The simple interest on a sum for 5 years is two-fifth of the sum. The percentage interest rate per annum is then,

- $10$%
- $6$%
- $8$%
- $12\displaystyle\frac{1}{2}$%

#### Problem 7

A clock is started at noon. By 10 minutes past 5, the hour hand has turned through an angle of

- $155^0$
- $145^0$
- $150^0$
- $160^0$

#### Problem 8

The speed of a boat in still waters is 15 km/hr. It goes 30 km upstream and returns to the starting point downstream in 4 hrs 30 mins. The speed of current of the stream is,

- 8 km/hr
- 5 km/hr
- 10 km/hr
- 15 km/hr

#### Problem 9

Which of the following fractions lies between $\displaystyle\frac{3}{5}$ and $\displaystyle\frac{2}{3}$?

- $\displaystyle\frac{1}{15}$
- $\displaystyle\frac{1}{3}$
- $\displaystyle\frac{2}{5}$
- $\displaystyle\frac{31}{50}$

#### Problem 10

How many digits are required for numbering the pages of a 300 page book ?

- 492
- 792
- 789
- 299

To know how to solve the problems quickly in mind and detailed explanation, you should refer to the corresponding solution set, **WBCS Main Arithmetic solution set 9.**

### Answers to the questions

**Problem 1.** Answer. Option c: $2$.

**Problem 2.** Answer: Option a: $33\displaystyle\frac{1}{3}$%.

**Problem 3.** Answer: Option d: 60.

**Problem 4.** Answer: Option d: $15:10:18$.

**Problem 5.** Answer: Option b: $\displaystyle\frac{9}{32}$.

**Problem 6.** Answer: Option c: $8$%.

**Problem 7.** Answer: Option a: $155^0$.

**Problem 8.** Answer: Option b: 5 km/hr.

**Problem 9.** Answer: Option d: $\displaystyle\frac{31}{50}$.

**Problem 10.** Answer: Option b: 792.

### 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**