MathsCBSE Class 10 · Basic · Sample paper, session 2026-27 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic sample paper 2026-27: question 4

From the official CBSE sample question paper for 2026-27, section A, question 4, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q4 · 1 mark · MCQPair of Linear Equations in Two Variables

The sum of the numerator and denominator of a fraction is 11. If the denominator is increased by 1, the fraction becomes $\frac{1}{2}$ , then the fraction is

(A) $\frac{2}{9}$
(B) $\frac{3}{8}$
(C) $\frac{4}{7}$
(D) $\frac{5}{6}$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

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

Hint 1

Let the numerator be x and the denominator be y.

Hint 2

Write one equation for the sum and one for the new fraction, then solve them together.

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 $\frac{x}{y}$ . Then $x + y = 11$ and $\frac{x}{y + 1} = \frac{1}{2}$ , so $2 x = y + 1$ .
Substituting gives $3 x = 12$ , so $x = 4$ and $y = 7$ . The fraction is $\frac{4}{7}$ . Option (C).
1 mark

Answer: 4/7, option (C)

Where the marks are

Forms both equations and solves to get 4/7 (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 paperSample paper 2026-27 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2026-27: question 4

Hints

Step-by-step solution

Revise the chapter

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