## Eleventh 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 eleventh 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 article**s 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**

### 11th WBCS Main level Arithmetic question set: time to answer: 10 mins

#### Problem 1

What will be the percentage markup on cost price to achieve a profit of 4% after 20% discount?

- 10%
- 35%
- 25%
- 30%

#### Problem 2

In a 200 litre solution of sugar fully dissolved in water, sugar is 20%. On heating for a while the solution gets more concentrated with sugar percentage increasing to 80% of the solution. What is the volume of water that evaporated?

- 140 litre
- 150 litre
- 130 litre
- 100 litre

#### Problem 3

At what time between 1 O'clock and 2 O'clock both minute hand and hour hand will be together?

- $5\displaystyle\frac{6}{11}$ minutes past 1 O'clock
- $5\displaystyle\frac{4}{11}$ minutes past 1 O'clock
- $5\displaystyle\frac{5}{11}$ minutes past 1 O'clock
- $5\displaystyle\frac{3}{11}$ minutes past 1 O'clock

#### Problem 4

The simple interest over 2 years at a certain interest rate on a certain amount is Rs. 2400. If the difference between the compound interest compounded annually at same rate over same period on same amount, and the simple interest be Rs. 138, what is the percentage interest rate per annum?

- 13.5%
- 10.5%
- 12.5%
- 11.5%

#### Problem 5

A basketful of oranges are counted in pairs, in 3s and in 5s, and every time one orange is left over. The least number of oranges in the basket is,

- 31
- 41
- 61
- 51

#### Problem 6

HCF of $\displaystyle\frac{12}{13}$ and $\displaystyle\frac{3}{5}$ is,

- $3$
- $12$
- $\displaystyle\frac{12}{65}$
- $\displaystyle\frac{3}{65}$

#### Problem 7

Two rational numbers lying between $\displaystyle\frac{4}{5}$ and $\displaystyle\frac{6}{7}$ are,

- $\displaystyle\frac{29}{35}$, $\displaystyle\frac{62}{70}$
- $\displaystyle\frac{28}{34}$, $\displaystyle\frac{35}{39}$
- $\displaystyle\frac{29}{35}$, $\displaystyle\frac{5}{6}$
- $\displaystyle\frac{65}{84}$, $\displaystyle\frac{5}{6}$

#### Problem 8

What is the unit's digit of the product of all the prime numbers between 10 and 30?

- 7
- 9
- 3
- 1

#### Problem 9

Present ages (in years) of Romi and Runu are in the ratio of 5 : 6. Three years ago their ages were in the ratio 9 : 11. What will the ratio of their ages after 6 years from now?

- 6 : 7
- 1 : 2
- 7 : 8
- 3 : 4

#### Problem 10

Inlet pipes A and B can fill a tank independently in 15 mins and 12 mins respectively. If both are opened simultaneously and B is closed after 3 mins how much more time will A take to fill the tank?

- 6 mins
- 8 mins 15 secs
- 10 mins 30 secs
- 9 mins 15 secs

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 11.**

### Answers to questions

**Problem 1. ** **Answer:** Option d: 30%.

**Problem 2. Answer:** Option b: 150 litres.

**Problem 3. Answer:** Option c: $5\displaystyle\frac{5}{11}$ minutes past 1 O'clock.

**Problem 4. Answer:** Option d: 11.5%.

**Problem 5. Answer:** Option a: 31.

**Problem 6. Answer:** Option d: $\displaystyle\frac{3}{65}$.

**Problem 7. Answer:** Option c: $\displaystyle\frac{29}{35}$, $\displaystyle\frac{5}{6}$.

**Problem 8. Answer:** Option c: 3.

**Problem 9. Answer:** Option a: 6 : 7.

**Problem 10. Answer:** Option b: 8 mins 15 secs.

### 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**