MathsCBSE Class 10 · Standard · Board exam 2024, set 30/1/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2024: question 29

Set in the CBSE Class 10 board exam of 2024, paper 30/1/1, section C, question 29, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29 · 3 marks · Short answerCompetency-basedPair of Linear Equations in Two Variables

Three years ago, Rashmi was thrice as old as Nazma. Ten years later, Rashmi will be twice as old as Nazma. How old are Rashmi and Nazma now?

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/1/1.

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 3 years ago, and what will they be in 10 years?

Hint 2

Turn each sentence into one equation, then solve the pair by elimination.

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 Rashmi and Nazma be $x$ years and $y$ years.
Three years ago: $x - 3 = 3 (y - 3) \Rightarrow x - 3 y + 6 = 0$ ...(1)
1 mark
Ten years later: $x + 10 = 2 (y + 10) \Rightarrow x - 2 y - 10 = 0$ ...(2)
1 mark
Subtract (1) from (2): $(x - 2 y - 10) - (x - 3 y + 6) = 0 \Rightarrow y - 16 = 0 \Rightarrow y = 16$ .
Then from (2): $x = 2 (16) + 10 = 42$ .
Check: $39 = 3 \times 13$ ✓ and $52 = 2 \times 26$ ✓.
So Rashmi is 42 years old and Nazma is 16 years old.
1 mark

Answer: Rashmi: 42 years; Nazma: 16 years

Where the marks are

Forms $x - 3 = 3 (y - 3)$ (1 mark)
Forms $x + 10 = 2 (y + 10)$ (1 mark)
Solves to get $x = 42$ , $y = 16$ (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 paper2024 board paper, set 30/1/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 29

Hints

Step-by-step solution

Revise the chapter

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