# Reasoning - Arithmetical

Arithmetical reasoning contains calculation with special sense of reasoning. This reasoning chapter normally contains all the chapters from quantitative aptitude. So, it is one of the most interesting chapters in reasoning, because it contains both aptitude and reasoning. Arithmetic reasoning may contain the following chapters of aptitude −

- Time and work
- Time, speed, and distance
- Simple interest
- Compound interest
- Percentage
- Profit and loss
- Number system
- Average
- Ratio and proportion

Let’s explain a little bit of each type arithmetic reasoning under this heading −

**Time and work** − Problems on time and work will be of normal men work and men women work type problems. In such type of questions, we have to bring the number to 1 always. If it is given that 5 men can do a certain work in 10 days, and after this data it is mentioned that 10 men can take how many days to do the work then at first we have to find that, 1 man can do the job in how many days and then we can proceed further.

**Time speed and distance** − For problems regarding this chapter, there is one formula which we can use in this context i.e. distance = time x speed.

**Simple interest** − If P is taken as principal, R is taken as rate of interest, T is taken as time, and I is taken as interest then the relationship between them is

I = (P x T x R) / 100

**Compound Interest** − If P is principal, R is rate, amount is A and time is n years then if interest is −

Compounded annually : A = P (1 + R/100)^{n}

Compounded half yearly : A = P [1 + (R/2)/100]^{2n}

Compounded quarterly : A = P [1+(R/4)/100]^{4n}

**Percentage** − If it is mentioned that at a certain percent, it will be meant that many hundredths. Thus if we say a percent it means a hundredths, and will be written as a %.

**Profit and loss** − Profit = sale price – cost price and %profit = (profit x 100) / cost price

**Average** − The average is a measure of central point of a set of numbers. It is an estimation of where the centre point or weight of a set of number lies.

$Average = \frac{Sum \: of \: sets \: of \: N \: numbers}{N}$

$Weighted \: average = \frac{Sum \: of \: observations \times \: weight}{Sum \: of \: weights}$

**Number system** − It is very important in arithmetical reasoning to know about the numbers. It is considered as backbone of mathematics.

**Natural Numbers**− Natural numbers are called as counting numbers and are represented as 1, 2 , 3, 4, 5, 6,…**Whole Numbers**− Whole numbers are those numbers which start from 0 to infinity. i.e. 0, 1, 2 …0 is not a natural number.

**Integers**− If we connect positive numbers and negative numbers with zero then we got integers. Also we can define integers as negative numbers + whole numbers. i.e. {..., - 3, - 2, - 1, 0, 1, 2, 3, …}

There are also even numbers and odd numbers. An even number is that number which can be divided by 2 and an odd number is that number which cannot be divided by 2.

A prime number is that number which can be divided by only two numbers that is 1 and the number itself. The smallest prime number is 2. Other prime numbers under 50 are, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47.

**1** - Govt. has decided to connect Tripura and Delhi via a train service which is called ‘Tripura Sundari Express’ Two trains are running from Tripura and Delhi towards each other. Train from Tripura in covering a distance of 60 km takes 2 hours more than that of the train from Delhi. If Tripura train doubles its speed, then it would take 1 hour less than that of Delhi. Tripura train’s speed is?

**Options** −

**A** - 5

**B** - 10

**C** - 7

**D** - 8

**Answer** − Option B

**Explanation** − Let Tripura train's speed be X km/hr.

Then, 60/x - 60/2x = 3

6x = 60

x = 10 km/hr.

**2** - Creative constructors has hired some workers from Bihar. From those newly appointed workers if 10 men working 6 hours a day can do a work in 20 days. Then 8 men working 10 hours a day can do it in how many days?

**Options** −

**A** - 15

**B** - 14

**C** - 17

**D** - 18

**Answer** − Option A

**Explanation** − 10 men work for 6 hours so total 60 hours and work is done in 20 days. 8 men working 10 hours means total 80 hours and the work will be completed in = (60 x 20)/80 = 15 days.

**3** - Riyaz and Saqlain are two workers and they work for GPR pumps and pipes. Riyaz is twice as good a workman as Saqlain and together Riyaz and Saqlain finish a piece of work in 20 days. In how many days will Riyaz alone finish the work?

**Options** −

**A** - 90

**B** - 66

**C** - 30

**D** - 29

**Answer** − Option C

**Explanation** − If Riyaz takes x days to do a work then Saqlain takes 2x days to do the same work.

1/x + 1/2x = 1/20

3/2x = 1/20

x = 30 days

Hence, Riyaz alone can finish the work in 30 days.