Problems Based on Numbers - Arithmetic

Question (1) The sum of two numbers is 50. If one of the numbers is 20 then find the second number.

Solution

Given, Sum of two numbers = 50

And one of the two numbers = 20

Thus second number = ?

Let the second (unknown) number = x

Now, as per question,

Given number + unknown number = 50

⇒ 20 + x = 50

After transposing 20 to RHS (Right Hand Side), we get

⇒ x = 50 – 20

⇒ x = 30

Thus, unknown number = 30 Answer

Check for the answer

Given number + unknown number = 50

⇒ 20 + 30 = 50

Thus, LHS = RHS. Hence proved.

Alternate Method to solve the problem

To solve this, deduct given number from the given sum

i.e. Sum of numbers – Given number

⇒ 50 – 20 = 30

Thus, Answer = 30

Question (2) When 55 is added to a number, it becomes 90, then find the number.

Solution

Given,

A number = 55

After adding another number to this given number, their sum = 90

Thus, the number = ?

Let the number =

Therefore, as per question,

Number + 55 = 90

⇒ x + 55 = 90

After transposing 55 to RHS, we get

x = 90 – 55

⇒ x = 35

Thus, number = 35 Answer

Check for the answer

A number + 55 = 90

⇒ 35 + 55 = 90

[∵ The number = 35 (As calculated above)]

Thus, LHS = RHS. Hence proved.

Alternate Method to solve the problem

To solve this, deduct the given number from the given sum

i.e. Sum of numbers – Given number

⇒ 90 – 55 = 35

Thus, Answer = 35

Question (3) If the sum of two numbers is 150 and one of the number is 60 then find the second number.

Solution

Given, Sum of two numbers = 150

And one of the two numbers = 60

Thus second number = ?

Let the second (unknown) number = x

Now, as per question,

Given number + unknown number = 150

⇒ 60 + x = 150

After transposing 60 to RHS (Right Hand Side), we get

⇒ x = 150 – 60

⇒ x = 90

Thus, unknown number = 90 Answer

Check for the answer

Given number + unknown number = 150

⇒ 60 + 90 = 150

Thus, LHS = RHS. Hence proved.

Alternate Method to solve the problem

To solve this, deduct the given number from the given sum

i.e. Sum of numbers – Given number

⇒ 150 – 90 = 60

Thus, Answer = 90

Question (4) The sum of two numbers is 260, if one of the numbers is 110, find the other number.

Solution

Given, Sum of two numbers = 260

And one of the two numbers = 110

Thus second number = ?

Let the second (unknown) number = x

Now, as per question,

Given number + unknown number = 260

⇒ 110 + x = 260

After transposing 110 to RHS (Right Hand Side), we get

⇒ x = 260 – 110

⇒ x = 150

Thus, unknown number = 150 Answer

Check for the answer

Given number + unknown number = 260

⇒ 110 + 150 = 260

Thus, LHS = RHS. Hence proved.

Alternate Method to solve the problem

To solve this, deduct the given number from the given sum

i.e. Sum of numbers – Given number

⇒ 260 – 110 = 150

Thus, Answer = 150

Question (5) If 65 is added to a number, it becomes 190. Thus what is the number?

Solution

Given,

A number = 65

After adding of another number to this given number, their sum = 190

Thus, the number = ?

Let the number =

Therefore, as per question,

Number + 65 = 190

⇒ x + 65 = 190

After transposing 65 to RHS, we get

x = 190 – 65

⇒ x = 125

Thus, number = 125 Answer

Check for the answer

A number + 125 = 190

⇒ 125 + 65 = 190

[∵ The number = 125 (As calculated above)]

Thus, LHS = RHS. Hence proved.

Alternate Method to solve the problem

To solve this, deduct given number from the given sum

i.e. Sum of numbers – Given number

⇒ 190 – 65 = 125

Thus, Answer = 125

If a number and difference between two numbers are given, then finding the other number

Question (6) The difference between the two numbers is 90. If one of the numbers is 50, find the other number.

Solution

Given,

Difference between two numbers = 90

And one of the numbers = 50

Thus, another number = ?

Let the another number = x

Now, as per question,

Number – Given number = 90

⇒ x – 50 = 90

After transposing –50 to the RHS.

[When a negative number is transposed to another side, its sign changes to positive. This means –50 becomes +50 after transposing from LHS to the RHS]

= 90 + 50

⇒ x = 140

Thus, required number = 140 Answer

Check for the answer

As per question,

Difference between two numbers = 90

This means, Number – Given number = 90

⇒ 140 – 50 = 90

[The required number = 140 (as calculated above)]

Thus, LHS = RHS. Hence proved.

Alternate Method

As given difference between two numbers = 90, and one of the number = 50

Thus, second number = Difference between numbers + One of the numbers

⇒ Second number = 90 + 50 = 140

Thus, required second number = 140 Answer

Question (7) The difference between the two numbers is 450. If one of the numbers is 150, find the other number.

Solution

Given,

Difference between two numbers = 450

And one of the numbers = 150

Thus, another number = ?

Let the another number = x

Now, as per question,

Number – Given number = 450

⇒ x – 150 = 450

After transposing –150 to the RHS.

[When a negative number is transposed to another side, its sign changes to positive. This means –150 becomes +150 after transposing from LHS to the RHS]

⇒ x = 450 + 150

⇒ x = 600

Thus, required number = 600 Answer

Check for the answer

As per question,

Difference between two numbers = 450

This means, Number – Given number = 450

⇒ 600 – 150 = 450

[The required number = 600 (as calculated above)]

Thus, LHS = RHS. Hence proved.

Alternate Method

As given difference between two numbers = 90, and one of the number = 50

Thus, second number = Difference between numbers + One of the numbers

⇒ Second number = 450 + 150 = 600

Thus, required second number = 600 Answer

Question (8) If 75 is subtracted from a number, the result is 95, then find the number.

Solution

Given,

Difference between two numbers = 95

One of the number = 75

Thus, the second number = ?

Let the another (second) number = x

Now, as per question,

Number – Given number = 95

⇒ x – 75 = 95

After transposing –75 to the RHS.

[When a negative number is transposed to another side, its sign changes to positive. This means –75 becomes +75 after transposing from LHS to the RHS]

⇒ x = 95 + 75

⇒ x = 170

Thus, required number = 170 Answer

Check for the answer

As per question,

Difference between two numbers = 95

This means, Number – Given number = 95

⇒ 170 – 75 = 95

[The required number = 170 (as calculated above)]

Thus, LHS = RHS. Hence proved.

Alternate Method

As given difference between two numbers = 95, and one of the number = 75

Thus, second number = Difference between numbers + One of the numbers

⇒ Second number = 95 + 75 = 170

Thus, required second number = 170 Answer

Question (9) If 40 is subtracted from a number, the result is 200, then find the number.

Solution

Given,

Difference between two numbers = 200

One of the number = 40

Thus, the second number = ?

Let the another (second) number = x

Now, as per question,

Number – Given number = 200

⇒ x – 40 = 200

After transposing –40 to the RHS.

[When a negative number is transposed to another side, its sign changes to positive. This means –40 becomes +40 after transposing from LHS to the RHS]

⇒ x = 200 + 40

⇒ x = 240

Thus, required number = 240 Answer

Check for the answer

As per question,

Difference between two numbers = 200

This means, Number – Given number = 200

⇒ 240 – 40 = 200

[The required number = 240 (as calculated above)]

Thus, LHS = RHS. Hence proved.

Alternate Method

As given difference between two numbers = 200, and one of the number = 40

Thus, second number = Difference between numbers + One of the numbers

⇒ Second number = 200 + 40 = 240

Thus, required second number = 240 Answer