MathsCBSE Class 10 · Basic · Board exam 2024, set 430/3/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2024: question 35(b)

Set in the CBSE Class 10 board exam of 2024, paper 430/3/1, section D, question 35(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q35(b) · 5 marks · Long answerPair of Linear Equations in Two Variables

The sum of the digits of a 2-digit number is $9$ . Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/3/1.

Hints

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

Hint 1

Write a 2-digit number with tens digit $y$ and ones digit $x$ as $10 y + x$ .

Hint 2

The reversed number is $10 x + y$ . Write one equation from the sum of the digits and one from 'nine times = twice the reversed number'.

Hint 3

Simplify the second equation to express $x$ in terms of $y$ , then substitute into the first.

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.

Let the digit in the ones place be $x$ and the digit in the tens place be $y$ .
Then the number is $10 y + x$ .
Sum of the digits: $x + y = 9$ ...(1)
1 mark
The reversed number is $10 x + y$ .
Given condition: $9 (10 y + x) = 2 (10 x + y)$
1 mark
Simplify the condition:
$90 y + 9 x = 20 x + 2 y$
$88 y = 11 x$
$\Rightarrow x = 8 y$ ...(2)
1 mark
Substitute (2) in (1):
$8 y + y = 9 \Rightarrow y = 1$ , so $x = 8$ .
1 mark
The required number is $10 (1) + 8 = 18$ .
Check: $9 \times 18 = 162 = 2 \times 81$ ✓
1 mark

Answer: The number is 18

Where the marks are

Forms $x + y = 9$ (1 mark)
Forms $9 (10 y + x) = 2 (10 x + y)$ (1 mark)
Simplifies to $x = 8 y$ (1 mark)
Solves to get $x = 8$ , $y = 1$ (1 mark)
States the number is 18 (1 mark)

Revise the chapter

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

Practise this chapterBoard-style questions from Pair of Linear Equations in Two Variables, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 430/3/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2024: question 35(b)

Hints

Step-by-step solution

Revise the chapter

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