# Sum of two numbers is 40 and their difference is 10. Find the numbers.

Arithmetic is a branch of mathematics that deals with numerals, number system, and their operations from ancient times. The term was originally derived from the Greek word “arithmos” which simply means numbers. It is preferred to get a definite single value. The traditional methods of arithmetic operations are constituent of addition, difference, multiplication, and division. These operations are being carried out for the purpose of human social and economical development for centuries.

**History of Arithmetic**

- The 17th-century Indian mathematician Brahmagupta is the “father of arithmetic”.
- Carl Friedrich Gauss in 1801, provided the Fundamental principle of number theory.

Arithmeticis the elementary branch of mathematics that specifically deals with the study of numbers and properties of traditional operations like addition, subtraction, multiplication, and division.

Besides the traditional operations of addition, subtraction, multiplication, and division arithmetic also include advanced calculating methods for percentage, logarithm, exponentiation and square roots, etc.

### Types of Basic Operations in Arithmetic

The four basic operations of arithmetic are discussed below-

**Addition (+)**

Addition or also known as summation is an operation to combine two or more values or numbers into a single value. The process of adding n number of values is called summation.

0 is considered as the identity element of addition as while adding 0 to any value gives the same result. For example, if we add 0 to 5 the result would be the same that is 5.

0 + 3 = 3

And, the addition of the opposite value of the same number is said to be an inverse element. The result of the addition of inverse elements is an identity element that is 0. For example, if we add 2 with its opposite value -5, then the result would be

5 + (-5) = 0

**Subtraction (-)**

The arithmetic operation determines the difference between two values (i.e. minuend minus the subtrahend) is subtraction. In the cases, where the minuend is greater than the subtrahend, the difference is positive. It is the inverse of addition.

9 – 3 = 6

While, if the subtrahend is greater than minuend the difference between them will be negative.

3 – 9 = -6

**Multiplication (×)**

Multiplication is the operation that combines the two values that is multiplicand and multiplier to give a single product. The two values involved in the operation of multiplication are known as multiplicand and multiplier.

The product of two values supposedly x and y are expressed in x.y or x×y form.

**Division (÷)**

The division is the operation that computes the quotient of two numbers. It is the inverse of multiplication. The two values involved in it are known as dividends by the divisor and if the quotient is more than 1 if the dividend is greater than the divisor the result would be a positive number.

10/5 = 2

### Sum of two numbers is 40 and their difference is 10. Find the numbers

**Answer:**

Let the two numbers be x and y.

According to the question,

x + y = 40……(i)

x – y = 10……..(ii)

Now, to know the value of one of the variables we need to solve one of the equations given above and substitute the value in the other equation.

Now, from equation (i) we can obtain the value of x by isolating it.

=>x = 40 – y

Then, substituting the value of x in equation (ii)

=>40 – y – y = 10

=>40 – 2y = 10

=>y = 30/2

=>y = 15

Substituting the value of y = 15 in x = 40 – y

=>x = 40 – 15 = 25

Hence, the two variables are x = 25 and y = 15.

### Similar Questions

**Question 1: The sum of two numbers is 8 and their difference is 4. Find the variables.**

**Answer:**

Let the two numbers be x and y.

According to the question,

x + y = 8…….(i)

x – y = 4……(ii)

Now, to know the value of one of the variables we need to solve one of the equations given above and substitute the value in the other equation.

Now, from equation (i) we can obtain the value of x by isolating it.

=>x = 8 – y

Then, substituting the value of x in equation (ii)

=>8 – y – y = 4

=>8 – 2y = 4

=>-2y = -4

=>y = -4/-2 = 2

Substituting the value of y = 2 in x = 8 – y

=>x = 8 – 2 = 6

Hence, the two variables are x = 6 and y = 2.

**Question 2: If the sum of two numbers is 95 and one exceeds the other by 15. What are the numbers?**

**Answer:**

Let the two numbers be x and x + 15

Now, according to the question,

=>x + x + 15 = 95

=>2x = 95 – 15

=>2x = 80

x = 80/2 = 40

If the first number is x = 40. Then, the value of the second number is given by

=>x + 15 = 40 + 15 = 55

Therefore, the two numbers are 40 and 55.

**Question 3: The sum of the two numbers is 25 and the difference is 13. Find the numbers.**

**Answer:**

Let the two numbers be x and y.

According to the question,

x + y = 25……(i)

x – y = 13……(ii)

Now, to know the value of one of the variables we need to solve one of the equations given above and substitute the value in the other equation.

Now, from equation (i) we can obtain the value of x by isolating it.

=>x = 25 – y

Then, substituting the value of x in equation (ii)

=>25 – y – y = 13

=>25 – 2y = 13

=>2y = 25 – 13

=>2y = 12

=>y = 38/2 = 6

Substituting the value of y = 6 in x = 25 – y

=>x = 25 – 6 = 19

Hence, the two variables are x = 19 and y = 6.

**Question 4: If the sum of two non-zero numbers is 8 and their difference is 7. Find the value of numbers.**

**Answer:**

Let the two numbers be x and y.

According to the question,

x + y = 25……(i)

x – y = 7……(ii)

Now, from equation (i) we can obtain the value of x by isolating it.

=>x = 25 – y

Then, substituting the value of x in equation (ii)

=>25 – y – y = 7

=>25 – 2y = 7

=>2y = 25 – 7

=>2y = 18

=>y = 18/2 = 9

Substituting the value of y = 9 in x = 25 – y

=>x = 25 – 9 = 16

Hence, the two variables are x = 16 and y = 9.