Linear equation in single variable MCQ Quiz - Objective Question with Answer for Linear equation in single variable - Download Free PDF

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.

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 ⇒ $\frac{5(x+7)}{3}$ - 4 = 16

Calculation:

$\frac{5(x+7)}{3}$- 4 = 16

⇒ 5(x + 7) - 12 = 16 × 3 

⇒ 5x + 35 - 12 = 48 

⇒ 5x + 23 = 48 

x = 5

Hence, the original number is 5.

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 ⇒ $\frac{5(x+7)}{3}$ - 4 = 16

Calculation:

$\frac{5(x+7)}{3}$- 4 = 16

⇒ 5(x + 7) - 12 = 16 × 3 

⇒ 5x + 35 - 12 = 48 

⇒ 5x + 23 = 48 

x = 5

Hence, the original number is 5.

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 ⇒ $\frac{5(x+7)}{3}$ - 4 = 16

Calculation:

$\frac{5(x+7)}{3}$- 4 = 16

⇒ 5(x + 7) - 12 = 16 × 3 

⇒ 5x + 35 - 12 = 48 

⇒ 5x + 23 = 48 

x = 5

Hence, the original number is 5.

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.