Whether you want to attain your dream of higher education or want to secure a high profile job, qualifying for competitive exams has now become essential for everything. Along with the English and Logical Reasoning section, the Arithmetic Reasoning (AR) section is also a part of various competitive exams. The arithmetic reasoning section includes a variety of questions that are based on mathematical concepts, thus, students often find it difficult to solve such questions. If you are preparing for AR, go through this blog which aims to help you understand these concepts better.

##### This Blog Includes:

## What is Arithmetic Reasoning?

When you are acquainted with the concepts of arithmetic reasoning, you will be able to easily solve any question. The AR questions do not involve complex calculations rather the questions tend to play with your mind with the tricky concept and language. You can practice the questions easily by using simple mathematical operations, arithmetic operations etc.

## Arithmetic Reasoning Topics

Listed below are the main topics under Arithmetic Reasoning-

- Algebra
- Ratio and Proportion
- Percentage
- HCF and LCM
- Ages
- Games and Tournaments
- Sequence and Patterns

## Solved Examples for AR

Now that you are familiar with the basics of Arithmetic Reasoning, let us go through some solved examples to understand the concept in a better way.

**Example 1:** Riya is 2 times older than Priya. 3 years ago, the sum of their current ages will be 66. What are their present ages?

**Solution: **

Let us begin by assuming their ages

Assume that Riya’s age is *x*

Its is given that the Priya is twice as old as Riya, then, Priya’s age will be 2*x *

After 3 years,

Riya’s age= x + 3

Priya’s age= 2x + 3

Their total sum is 66

Hence, the equation becomes,

x+ 3 + 2x + 3= 66

3x + 6 = 66

3x= 66- 6

3x = 60

x= 60/ 3

x= 20

*So, the age current age of Riya is 20 and that of Priya is 40*

**Example 2:** Find the number which when multiplied by 3/4th of itself gives out the value 10800.

**Solution: **

Let us begin by assuming that the number is y

Then 3/4th of y would be (y x 3/4)

As per the question,

y x (y x 3/4) = 10800

3/4 y 2= 10800

y 2= 10800 x 4/3

y 2= 14400

y = 14400

y = 120

*Find Out How Smart Are you With These Trick Questions!*

**Example 3:** Rahul is now 1/4th times as old as his mother Radha. Four years hence, his mother will be three times as old as her son. The age of his mother Radha (in years) is-

**Solution:** Let Rahul’s mother Radha age be 4x years. Then, Rahul’s age = x years.

Four years hence, Rahul’s age = (x + 4) years and Rahul’s mother Radha’s age = (4x + 4) years.

So, 4x+4= 3 (x+4)

4x-3x= 12-4;

x = 8.

Rahul’s mother Radha’s age = 4x= 4 x 8=32 years

**Example 4: **A monkey climbs 30 feet at the beginning of each hour and rests for a while when he slips back 20 feet before he again starts climbing at the beginning of the next hour. If he begins his ascent at 8.00 a.m., at what will he first touch a flag at 120 feet from the ground?

**Solution: **Let ascent of the monkey in 1 hour = ( 30 – 20 ) = 10 feet.

So, the monkey ascends 90 feet in 9 hours i.e., 5 p.m.

Clearly, in the next 1 hour i.e., till 6 p.m.

The monkey ascends the remaining 30 feet to touch the flag.

**Example 5: **Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A?

**Solution: **

Let Rs. x be the fare of city B from city A and Rs. y be the fare of city C from city A. Then,

2x + 3y = 77 …(i)

3x + 2y = 73 …(ii)

Multiplying (i) by 3 and (ii) by 2 and subtracting, we get: 5y = 85 or y= 17. Putting y = 17 in (i), we get : x = 13

**Example 6:** A girl counted in the following way on the fingers of her left hand: She started by calling the thumb 1, the index finger 2, middle finger 3, ring finger 4, little finger 5 and then reversed direction calling the ring finger 6, middle finger 7 and so on. She counted up to 1994. She ended up counting on which finger?

**Solution: **While counting the numbers associated to the thumb will be 1,9,17,25,………

i.e., numbers of the form (8n + 1 )

Since 1994 = 249 × 8 + 2

So, 1993 shall correspond to the thumb and 1994 to the index finger.

*We hope that after these solved examples, you will be able to solve the below-mentioned Arithmetic Reasoning questions. *

## Arithmetic Reasoning Questions

Let us quickly solve these below mentioned questions-

- Some classmates had planned to purchase the photocopy of an assignment together which caused them rupees 96. When all of them were going to buy it, 4 friends did not show up, hence, everyone had to pay Rs. 4 extra. Determine the number of friends that were present while purchasing the assignment
- A waiter’s monthly income consists of salary as well as some tips. For one month his steps were ¾ of his salary. Determine his income by tips in terms of the fraction
- A teacher was explaining to the students how to count on the fingers, so she began by calling thumb 1, index finger 2, middle finger 3, ring finger 4 and little finger 5. Then she went on with the reverse order in which she stated ring finger 6, middle finger 7 and so on. She taught the children to count up to 1994. Find out on which finger did she stopped the counting?
- In the SSC CGL exam, Sneha attempted 60 questions in total and secured 130 marks. For every correct answer, she got 4 marks and lost one mark for every incorrect answer. as per the total marks received to determine the number of questions she attempted correctly
- What would be the product of all the numbers that one could possibly dial on a telephone?
- 30 friends decide to play a badminton tournament of single players. Once the player is out he or she is out of the tournament. Calculate the number of matches that has to be played to determine who is the winner of the tournament.
- Rohit attempted an examination in which he got two eyes as many sums wrong as he got right. If he attempted 48 questions in total, how many questions did he solve correctly?
- In a farm full of cows and hens, there are 14 legs more than twice the number of heads. How many cows are there in the farm?

## Arithmetic Reasoning

## Arithmetic Reasoning for Bank Exams

- The price of rice has increased by 20%. Rohan has decided to spend only 8% more than what he initially did on buying rice. What is the percentage decrease in Rohan’s rice consumption?
- Aakriti is a working and Anukriti is a sleeping partner in a business. Aakriti puts in Rs. 20000 and Anukriti puts in Rs. 30000. Aakriti receives 15% of the profit for managing the business, and the rest is divided in proportion to their capitals. If the total profit is Rs. 10500, then find the share of Anukriti in the profit.
- A is 3 years older to B and 3 years younger to C, while B and D are twins. How many years older is C and D?
- A, B, C, D and E play a game of cards. A says to B, “If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has.” A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards be 133, how many cards does B have?
- The price of rice has increased by 20%. Lalu has decided to spend only 8% more than what he initially did on buying rice. What is the percentage decrease in Lalu’s rice consumption?
- The sum of the ages of Kidambi and Srikanth 14 years hence will be equal to 2 times their present age. If at present Kidambi is 8 years elder to Srikanth, then what are their present ages?
- Between two book ends in your study are displayed your five favourite puzzle books. If you decide to arrange the five books in every possible combination and moved just one book every minute, how long would it take you?
- Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A?

## Arithmetic Reasoning for SSC Exams

- What will be the product of all the numbers on a telephone?
- Find the remainder when 231 is divided by 5?
- If ‘+’ means ‘minus’ ‘×’ means ‘divided by’ ‘÷’ means ‘plus’ and ‘–’means ‘multiplied by’ then which of the following will be the value of expression 7 × 3.5 ÷ 2 – 4 + 5 ?
- If signs + and –and numbers 4 and 8 interchanges with each other, which one of the following four equations would be correct?
- I have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I have to pack and distribute?
- 12 years old Shyaam is three times as old as his brother Rithav. How old will Shyaam be when he is twice as old as Rithav?
- A father is now three times as old as his son. 5 years ago, he was four times as old as his son. What is the age of the son now?
- The 30 members of a club decided to play a badminton singles tournament. Every time a member loses a game he is out of the tournament. There are no ties. What is the minimum number of matches that must be played to determine the winner?

We hope that through this blog, you are now all clear about the important concept of Arithmetic Reasoning. If you want to seek top-notch career advice for kick-starting your career abroad, reach out to our experts at **Leverage Edu**.