CBSE Class 10 Mathematics Standard sample paper 2023-24: question 28(a)

Hints

Open one hint at a time and try again before the next.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. Let the tens digit be $x$ and the units digit be $y$.

   The number is $10x+y$. The number with its digits reversed is $10y+x$.

   ½ mark

2. Given condition: $(10x+y)+(10y+x)=66$

   $\Rightarrow 11(x+y)=66\Rightarrow x+y=6$ ...(1)

   ½ mark

3. The digits differ by 2, so either $x-y=2$ ...(2)

   ½ mark

4. or $y-x=2$ ...(3)

   ½ mark

5. Case 1: adding (1) and (2) gives $2x=8$, so $x=4$ and $y=2$. The number is 42.

   ½ mark

6. Case 2: adding (1) and (3) gives $2y=8$, so $y=4$ and $x=2$. The number is 24.

   So there are two such numbers: 42 and 24.

   ½ mark

Answer: The number is 42 or 24; there are 2 such numbers

Revise the chapter

• Chapter: Pair of Linear Equations in Two Variables (notes, formulas, where marks are lost and every past question)