MathsCBSE Class 10 · Standard · Board exam 2024, set 30/3/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2024: question 32(a)

Set in the CBSE Class 10 board exam of 2024, paper 30/3/1, 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

In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100 km/h and by doing so, the time of flight is increased by 30 minutes. Find the original duration of the flight.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/3/1.

Hints

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

Hint 1

Write the time taken at the original speed x and at the reduced speed x – 100 in terms of x.

Hint 2

The difference of the two times is 30 minutes = 1/2 hour. Form the quadratic and factorise. Remember that the question asks for the time, not the speed.

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 speed be $x$ km/h. The reduced speed is $(x - 100)$ km/h. Time = distance ÷ speed, and 30 min $= \frac{1}{2}$ h. So $\frac{2800}{x - 100} - \frac{2800}{x} = \frac{1}{2}$ .
2 marks
$2800 \cdot \frac{x - ( x - 100 )}{x ( x - 100 )} = \frac{1}{2} \Rightarrow 560000 = x^{2} - 100 x \Rightarrow x^{2} - 100 x - 560000 = 0$ .
½ mark
$x^{2} - 800 x + 700 x - 560000 = 0 \Rightarrow (x - 800) (x + 700) = 0$ .
1 mark
$x = 800$ or $x = - 700$ . Speed cannot be negative, so $x = 800$ km/h.
½ mark
Original duration $= \frac{2800}{800} = \frac{7}{2}$ h $= 3$ h 30 min.
1 mark

Answer: Original duration = 3.5 hours (3 h 30 min)

Where the marks are

Forms the equation $\frac{2800}{x - 100} - \frac{2800}{x} = \frac{1}{2}$ (2 marks)
Reduces it to $x^{2} - 100 x - 560000 = 0$ (½ mark)
Factorises as $(x - 800) (x + 700) = 0$ (1 mark)
Rejects the negative value and takes $x = 800$ (½ mark)
Finds the original duration $\frac{7}{2}$ h (1 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 paper2024 board paper, set 30/3/1 (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.

CBSE Class 10 Mathematics Standard 2024: question 32(a)

Hints

Step-by-step solution

Revise the chapter

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