Linear equation in single variable MCQ Quiz - Objective Question with Answer for Linear equation in single variable - Download Free PDF
Last updated on Jun 13, 2025
Latest Linear equation in single variable MCQ Objective Questions
Linear equation in single variable Question 1:
A two digit number is such that the sum of the digits is 9. When the number with the same digits are reversed is subtracted from the original number, the difference is 27. What is the original number?
Answer (Detailed Solution Below)
Linear equation in single variable Question 1 Detailed Solution
Given:
Sum of the digits of a two-digit number = 9
Original number - Reversed number = 27
Formula used:
A two-digit number can be represented as 10x + y, where x is the tens digit and y is the units digit.
Calculations:
Let the original number be 10x + y
The sum of the digits: x + y = 9 --- (1)
The number with digits reversed will be 10y + x
When the reversed number is subtracted from the original number, the difference is 27:
(10x + y) - (10y + x) = 27
10x + y - 10y - x = 27
9x - 9y = 27
x - y = 3 --- (2)
Add equation (1) and (2):
(x + y) + (x - y) = 9 + 3
2x = 12
⇒ x = 6
Substitute x = 6 into equation (1):
6 + y = 9
⇒ y = 3
The original number = 10x + y = 10(6) + 3 = 60 + 3 = 63
∴ The correct answer is option 4.
Linear equation in single variable Question 2:
7 is added to a certain number and the sum is multiplied by 5. The product is then divided by 3 and 4 is subtracted from the quotient. If the result comes to 16, then what is the original number?
Answer (Detailed Solution Below)
Linear equation in single variable Question 2 Detailed Solution
Given:
7 is added to a certain number and the sum is multiplied by 5. The product is then divided by 3 and 4 is subtracted from the quotient. If the result comes to 16.
Concept used:
Let the number be = x
7 is added to a certain number and the sum is multiplied by 5 ⇒ (x +7) × 5
The product is then divided by 3 and 4 is subtracted from the quotient and the result is 16 ⇒ \(5(x+7)\over 3\) - 4 = 16
Calculation:
\(5(x+7)\over 3\)- 4 = 16
⇒ 5(x + 7) - 12 = 16 × 3
⇒ 5x + 35 - 12 = 48
⇒ 5x + 23 = 48
x = 5
Hence, the original number is 5.
Top Linear equation in single variable MCQ Objective Questions
7 is added to a certain number and the sum is multiplied by 5. The product is then divided by 3 and 4 is subtracted from the quotient. If the result comes to 16, then what is the original number?
Answer (Detailed Solution Below)
Linear equation in single variable Question 3 Detailed Solution
Download Solution PDFGiven:
7 is added to a certain number and the sum is multiplied by 5. The product is then divided by 3 and 4 is subtracted from the quotient. If the result comes to 16.
Concept used:
Let the number be = x
7 is added to a certain number and the sum is multiplied by 5 ⇒ (x +7) × 5
The product is then divided by 3 and 4 is subtracted from the quotient and the result is 16 ⇒ \(5(x+7)\over 3\) - 4 = 16
Calculation:
\(5(x+7)\over 3\)- 4 = 16
⇒ 5(x + 7) - 12 = 16 × 3
⇒ 5x + 35 - 12 = 48
⇒ 5x + 23 = 48
x = 5
Hence, the original number is 5.
Linear equation in single variable Question 4:
7 is added to a certain number and the sum is multiplied by 5. The product is then divided by 3 and 4 is subtracted from the quotient. If the result comes to 16, then what is the original number?
Answer (Detailed Solution Below)
Linear equation in single variable Question 4 Detailed Solution
Given:
7 is added to a certain number and the sum is multiplied by 5. The product is then divided by 3 and 4 is subtracted from the quotient. If the result comes to 16.
Concept used:
Let the number be = x
7 is added to a certain number and the sum is multiplied by 5 ⇒ (x +7) × 5
The product is then divided by 3 and 4 is subtracted from the quotient and the result is 16 ⇒ \(5(x+7)\over 3\) - 4 = 16
Calculation:
\(5(x+7)\over 3\)- 4 = 16
⇒ 5(x + 7) - 12 = 16 × 3
⇒ 5x + 35 - 12 = 48
⇒ 5x + 23 = 48
x = 5
Hence, the original number is 5.
Linear equation in single variable Question 5:
A two digit number is such that the sum of the digits is 9. When the number with the same digits are reversed is subtracted from the original number, the difference is 27. What is the original number?
Answer (Detailed Solution Below)
Linear equation in single variable Question 5 Detailed Solution
Given:
Sum of the digits of a two-digit number = 9
Original number - Reversed number = 27
Formula used:
A two-digit number can be represented as 10x + y, where x is the tens digit and y is the units digit.
Calculations:
Let the original number be 10x + y
The sum of the digits: x + y = 9 --- (1)
The number with digits reversed will be 10y + x
When the reversed number is subtracted from the original number, the difference is 27:
(10x + y) - (10y + x) = 27
10x + y - 10y - x = 27
9x - 9y = 27
x - y = 3 --- (2)
Add equation (1) and (2):
(x + y) + (x - y) = 9 + 3
2x = 12
⇒ x = 6
Substitute x = 6 into equation (1):
6 + y = 9
⇒ y = 3
The original number = 10x + y = 10(6) + 3 = 60 + 3 = 63
∴ The correct answer is option 4.