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PQ XY BC, AP = 2 cm, PX = 1.5 cm… (Class 10 Maths 2025, Q6)

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MathsCBSE Class 10 · Standard · Board exam 2025, set 30/6/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2025: question 6

Set in the CBSE Class 10 board exam of 2025, paper 30/6/1, section A, question 6, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q6 · 1 mark · MCQTriangles

In the adjoining figure, PQ || XY || BC, AP = 2 cm, PX = 1.5 cm and BX = 4 cm. If QY = 0.75 cm, then AQ + CY =

  1. (A)6 cm
  2. (B)4.5 cm
  3. (C)3 cm
  4. (D)5.25 cm

Figure in the paper: A triangle ABC with A at the top and B, C at the base. Points P and X lie on side AB (P above X), and Q and Y lie on side AC (Q above Y). Segments PQ, XY and BC are drawn parallel to each other, horizontal, with arrows marking the parallel lines. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/6/1.

Hints

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

Hint 1

Parallel lines divide the two sides in the same ratio.

Hint 2

Compare AP : PX with AQ : QY, and PX : XB with QY : YC.

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.

  1. In , , so by BPT : , giving cm.

    ½ mark

  2. In trapezium -type section, the parallel lines cut the sides proportionally: : , so cm. Hence cm. Option (C).

    ½ mark

Answer: 3 cm, option (C)

Where the marks are

  • Finds AQ = 1 cm by BPT (½ mark)
  • Finds CY = 2 cm and total 3 cm (½ mark)

Revise the chapter

Practise this chapterBoard-style questions from Triangles, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 30/6/1 (Standard): 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.