Problems Based on Numbers
Finding the number when one number and sum of two numbers given
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 of another number to this given number, their sum = 90
Thus, the number = ?
Let the number = x
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 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 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 number 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 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 = x
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 other side, its sign changes to positive. This means –50 becomes +50 after transposing from LHS to the RHS]
⇒ x = 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 other 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 other 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 other 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
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