Let’s explore another problem that is commonly asked in the CBSE Class 9 exam pattern…

Question

The sum of the digits of a two-digit number is 9. If 27 is subtracted from the number, its digits are reversed. Find the number.

Solution

Step 1: Define the variables

Let the two-digit number be 10x+y10x + y, where:

• xx is the digit in the tens place.
• yy is the digit in the units place.

Step 2: Write the given conditions as equations

1. The sum of the digits is 9: x+y=9.(1)x + y = 9 \tag{1}.
2. If 27 is subtracted from the number, the digits are reversed: 10x+y−27=10y+x⇒9x−9y=27⇒x−y=3.(2)10x + y – 27 = 10y + x \quad \Rightarrow \quad 9x – 9y = 27 \quad \Rightarrow \quad x – y = 3 \tag{2}.

Step 3: Solve the equations

From equation (2): x−y=3⇒x=y+3.(3)x – y = 3 \quad \Rightarrow \quad x = y + 3 \tag{3}.

Substitute x=y+3x = y + 3 into equation (1): (y+3)+y=9.(y + 3) + y = 9. 2y+3=9⇒2y=6⇒y=3.2y + 3 = 9 \quad \Rightarrow \quad 2y = 6 \quad \Rightarrow \quad y = 3.

Substitute y=3y = 3 into equation (3): x=y+3=3+3=6.x = y + 3 = 3 + 3 = 6.

Step 4: Write the solution

The number is: 10x+y=10(6)+3=63.10x + y = 10(6) + 3 = 63.

Verification

1. The sum of the digits is: 6+3=96 + 3 = 9 (correct).
2. Subtracting 27 from 63 gives 63−27=3663 – 27 = 36, which is the reverse of 63 (correct).

This problem ensures the following are covered:

1. Algebraic representation of word problems.
2. Logical derivation and substitution.
3. Verification of the result.

Would you like me to graphically represent another scenario or explain additional examples? PLZ

COOMENT…..