MathsCBSE Class 10 · Basic · Board exam 2026, set 430/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2026: question 25

Set in the CBSE Class 10 board exam of 2026, paper 430/4/1, section B, question 25, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25 · 2 marks · Very short answerTriangles

In the given figure, $QR ∥ C B$ and $R P ∥ A C$ . If $B R = 10$ cm, $Q A = 12$ cm, $B P = 12$ cm and $P C = 18$ cm, then find the lengths of AR and QC.

Figure in the paper: Triangle ABC with apex A; R lies on AB, Q lies on AC, P lies on BC; QR is parallel to CB (horizontal); RP is parallel to AC. Given BR = 10 cm, QA = 12 cm, BP = 12 cm, PC = 18 cm. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/4/1.

Hints

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

Hint 1

Use the Basic Proportionality Theorem twice, once for each pair of parallel lines.

Hint 2

With RP ∥ AC, the sides BA and BC are divided in the same ratio.

Hint 3

Find AR first; then use it with QR ∥ CB to find QC.

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.

In $△ A B C$ , $R P ∥ A C$ , so by BPT: $\frac{B P}{P C} = \frac{B R}{R A} \Rightarrow \frac{12}{18} = \frac{10}{A R} \Rightarrow A R = 15$ cm
1 mark
In $△ A B C$ , $QR ∥ C B$ , so by BPT: $\frac{A R}{R B} = \frac{A Q}{QC} \Rightarrow \frac{15}{10} = \frac{12}{QC} \Rightarrow QC = 8$ cm
1 mark

Answer: AR = 15 cm, QC = 8 cm

Where the marks are

Applies BPT with $R P ∥ A C$ to get $A R = 15$ cm (1 mark)
Applies BPT with $QR ∥ C B$ to get $QC = 8$ cm (1 mark)

Revise the chapter

Chapter: Triangles (notes, formulas, where marks are lost and every past question)
Topic: Basic Proportionality Theorem (Thales Theorem)

Practise this chapterBoard-style questions from Triangles, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 430/4/1 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Basic 2026: question 25

Hints

Step-by-step solution

Revise the chapter

More questions from Triangles