NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.3 Question 2(iii)

NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.3 Question 2(iii)

Question:

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

Given:

Let the two-digit number be 10a + b, where a and b are the digits. The sum of the digits is 9, and nine times the number is twice the number obtained by reversing the order of the digits.

To Find:

The value of the two-digit number.

Formula:

Elimination method for solving linear equations.

Solution:

We have the following equations:

a + b = 9 ---(1)

9(10a + b) = 2(10b + a) ---(2)

From equation (1), we get a = 9 - b. Substituting this into equation (2):

9(10(9 - b) + b) = 2(10b + (9 - b))

⇒ 9(90 - 10b + b) = 2(10b + 9 - b)

⇒ 9(90 - 9b) = 2(9b + 9)

⇒ 810 - 81b = 18b + 18

⇒ 810 - 18 = 18b + 81b

⇒ 792 = 99b

⇒ b = 792 99 = 8

Substituting b = 8 into a = 9 - b, we get:

a = 9 - 8 = 1

Therefore, the two-digit number is 10a + b = 10(1) + 8 = 18

Result:

The two-digit number is 18.

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