NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Example 10

NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Example 10

Question:

The sum of a two-digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there? Use elimination method

Given:

Let the two-digit number be 10a + b, where a and b are digits. The reversed number is 10b + a. Their sum is 66, and |a - b| = 2.

To Find:

The two-digit number and the total number of such numbers.

Formula:

10a + b + 10b + a = 66

Solution:

10a + b + 10b + a = 66 ⇒ 11a + 11b = 66 ⇒ a + b = 6

Since |a - b| = 2, we have two cases:

Case 1:

a - b = 2. Solving a + b = 6 and a - b = 2 simultaneously, we get 2a = 8 ⇒ a = 4 and b = 2. The number is 42.

Case 2:

b - a = 2. Solving a + b = 6 and b - a = 2 simultaneously, we get 2b = 8 ⇒ b = 4 and a = 2. The number is 24.

Result:

The two-digit numbers are 42 and 24. There are 2 such numbers.

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