A fraction becomes 1/3, when 1 is subtracted from the numerator and it becomes 1/4, when 8 is added to its denominator. Find the fraction.

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/3/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2025: question 28(a)

Set in the CBSE Class 10 board exam of 2025, paper 430/3/1, section C, question 28(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28(a) · 3 marks · Short answerPair of Linear Equations in Two Variables

A fraction becomes $\frac{1}{3}$ , when 1 is subtracted from the numerator and it becomes $\frac{1}{4}$ , when 8 is added to its denominator. Find the fraction.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/3/1.

Hints

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

Hint 1

Call the numerator x and the denominator y, and write each condition as an equation.

Hint 2

Both equations have −y, so subtracting one from the other removes y.

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 fraction be $\frac{x}{y}$ .
½ mark
$\frac{x - 1}{y} = \frac{1}{3} \Rightarrow 3 x - 3 = y \Rightarrow 3 x - y = 3 ...(i)$
½ mark
$\frac{x}{y + 8} = \frac{1}{4} \Rightarrow 4 x = y + 8 \Rightarrow 4 x - y = 8 ...(ii)$
½ mark
Subtracting (i) from (ii): $x = 5$ . From (i): $y = 3 (5) - 3 = 12$ .
1 mark
The required fraction is $\frac{5}{12}$ .
½ mark

Answer: 5/12

Where the marks are

Assumes the fraction as x/y (½ mark)
Forms 3x − y = 3 (½ mark)
Forms 4x − y = 8 (½ mark)
Solves to get x = 5, y = 12 (1 mark)
States the fraction 5/12 (½ 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 paper2025 board paper, set 430/3/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 28(a)

Hints

Step-by-step solution

Revise the chapter

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