MathsCBSE Class 10 · Standard · Board exam 2026, set 30/4/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2026: question 32(a)

Set in the CBSE Class 10 board exam of 2026, paper 30/4/1, section D, question 32(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32(a) · 5 marks · Long answerCompetency-basedQuadratic Equations

A person on tour has ₹ 5,400 for his expenses. If he extends his tour by 5 days, he has to cut down his daily expenses by ₹ 180. Find the original duration of the tour and daily expense.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/4/1.

Hints

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

Hint 1

Let the original number of days be x; write the daily expense in both situations.

Hint 2

The difference of the two daily expenses is ₹180; this gives a quadratic equation in x.

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. Daily expense $= ₹ \frac{5400}{x}$ ; if extended to $x + 5$ days, daily expense $= ₹ \frac{5400}{x + 5}$ . Given: $\frac{5400}{x} - \frac{5400}{x + 5} = 180$ .
2 marks
$\frac{5400 \times 5}{x ( x + 5 )} = 180 \Rightarrow x (x + 5) = 150 \Rightarrow x^{2} + 5 x - 150 = 0$ .
1 mark
$x^{2} + 15 x - 10 x - 150 = 0 \Rightarrow (x + 15) (x - 10) = 0 \Rightarrow x = - 15$ or $x = 10$ .
1 mark
Number of days cannot be negative, so $x = 10$ .
½ mark
Original duration = 10 days and daily expense $= \frac{5400}{10} = ₹540$ .
½ mark

Answer: Original duration = 10 days; daily expense = ₹540

Where the marks are

Forms $\frac{5400}{x} - \frac{5400}{x + 5} = 180$ (2 marks)
Reduces to $x^{2} + 5 x - 150 = 0$ (1 mark)
Factorises to $(x + 15) (x - 10) = 0$ (1 mark)
Rejects negative root, $x = 10$ (½ mark)
States daily expense ₹540 (½ mark)

Revise the chapter

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

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 30/4/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 32(a)

Hints

Step-by-step solution

Revise the chapter

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