MathsCBSE Class 10 · Standard · Board exam 2026, set 30/2/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2026: question 33(a)

Set in the CBSE Class 10 board exam of 2026, paper 30/2/1, section D, question 33(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q33(a) · 5 marks · Long answerCompetency-basedQuadratic Equations

A person on a tour has ₹ 4,200 for expenses. If he extends his tour for 3 days, he has to cut down his daily expenses by ₹ 70. Find the original duration of the tour.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/2/1.

Hints

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

Hint 1

Write the daily expense as total money ÷ number of days, before and after the extension.

Hint 2

The old daily expense minus the new one equals ₹ 70; clear the fractions to get a quadratic.

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 original duration be x days. Original daily expense $= ₹ \frac{4200}{x}$ ; new daily expense $= ₹ \frac{4200}{x + 3}$ . Given: $\frac{4200}{x} - \frac{4200}{x + 3} = 70$
2 marks
$\frac{4200 \cdot 3}{x ( x + 3 )} = 70 \Rightarrow x (x + 3) = 180 \Rightarrow x^{2} + 3 x - 180 = 0$
1½ marks
$x^{2} + 15 x - 12 x - 180 = 0 \Rightarrow (x + 15) (x - 12) = 0 \Rightarrow x = - 15$ or $x = 12$
1 mark
Number of days cannot be negative, so reject $x = - 15$ . Original duration of the tour = 12 days.
½ mark

Answer: 12 days

Where the marks are

Forms equation $\frac{4200}{x} - \frac{4200}{x + 3} = 70$ (2 marks)
Reduces to $x^{2} + 3 x - 180 = 0$ (1½ marks)
Factorises to $(x + 15) (x - 12) = 0$ (1 mark)
Rejects −15 and gives 12 days (½ mark)

Revise the chapter

Chapter: Quadratic Equations (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Quadratic Equations, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/2/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 33(a)

Hints

Step-by-step solution

Revise the chapter

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