MathsCBSE Class 10 · Standard · Board exam 2026, set 30/3/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2026: question 34(b)

Set in the CBSE Class 10 board exam of 2026, paper 30/3/1, section D, question 34(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q34(b) · 5 marks · Long answerPair of Linear Equations in Two Variables

Five years ago, Adil was thrice as old as Bharat. Ten years later Adil shall be twice as old as Bharat. To know the present ages of Adil and Bharat : (i) form the linear equations representing the above information. (ii) show that the system of equations is consistent with unique solution. (iii) find the present ages of Adil and Bharat.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/3/1.

Hints

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

Hint 1

Let the present ages be x and y. What were they 5 years ago, and what will they be 10 years later?

Hint 2

Compare $a_{1} / a_{2}$ with $b_{1} / b_{2}$ : if they are unequal, the lines intersect at exactly one point.

Hint 3

Subtracting one equation from the other removes x directly.

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 present ages of Adil and Bharat be $x$ years and $y$ years respectively.
(i) Five years ago: $x - 5 = 3 (y - 5)$
$\Rightarrow x - 5 = 3 y - 15 \Rightarrow x - 3 y = - 10$ ...(1)
1 mark
Ten years later: $x + 10 = 2 (y + 10)$
$\Rightarrow x + 10 = 2 y + 20 \Rightarrow x - 2 y = 10$ ...(2)
1 mark
(ii) Write the equations as $x - 3 y + 10 = 0$ and $x - 2 y - 10 = 0$ .
Then $\frac{a _{1}}{a _{2}} = \frac{1}{1} = 1$ and $\frac{b _{1}}{b _{2}} = \frac{- 3}{- 2} = \frac{3}{2}$ .
Since $\frac{a _{1}}{a _{2}} \neq = \frac{b _{1}}{b _{2}}$ , the lines intersect at one point. So the system is consistent with a unique solution.
1 mark
(iii) Subtract (1) from (2):
$(x - 2 y) - (x - 3 y) = 10 - (- 10) \Rightarrow y = 20$
1 mark
Substitute $y = 20$ in (2): $x - 40 = 10 \Rightarrow x = 50$ .
So Adil is 50 years old and Bharat is 20 years old.
1 mark

Answer: (i) x − 3y = −10, x − 2y = 10; (ii) a₁/a₂ = 1 ≠ b₁/b₂ = 3/2, so consistent with a unique solution; (iii) Adil 50 years, Bharat 20 years

Where the marks are

Forms $x - 3 y = - 10$ (1 mark)
Forms $x - 2 y = 10$ (1 mark)
Compares ratios $a_{1} / a_{2} \neq = b_{1} / b_{2}$ and concludes a unique solution (1 mark)
Finds $y = 20$ (1 mark) and $x = 50$ (1 mark)

Revise the chapter

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

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 paper2026 board paper, set 30/3/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 34(b)

Hints

Step-by-step solution

Revise the chapter

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