MathsCBSE Class 10 · Basic · Board exam 2024, set 430/2/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2024: question 32

Set in the CBSE Class 10 board exam of 2024, paper 430/2/1, section D, question 32, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32 · 5 marks · Long answerQuadratic Equations

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was ₹ 750. Find the total number of toys produced on that day.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/2/1.

Hints

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

Hint 1

Let the number of toys be $x$ and write the cost of one toy in terms of $x$ .

Hint 2

Total cost = (number of toys) × (cost of one toy). Set this equal to 750.

Hint 3

Rearrange into a quadratic and factorise: look for two numbers with product 750 and sum 55.

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 number of toys produced that day be $x$ . Then the cost of each toy is ₹ $(55 - x)$ .
½ mark
Total cost $=$ number of toys $\times$ cost per toy: $x (55 - x) = 750$
1 mark
$55 x - x^{2} = 750 \Rightarrow x^{2} - 55 x + 750 = 0$
1 mark
Split the middle term, since $25 \times 30 = 750$ and $25 + 30 = 55$ : $x^{2} - 25 x - 30 x + 750 = 0 \Rightarrow x (x - 25) - 30 (x - 25) = 0 \Rightarrow (x - 25) (x - 30) = 0$
1½ marks
$x = 25$ or $x = 30$ . Both values give a total cost of ₹750 (25 × ₹30 or 30 × ₹25). So 25 or 30 toys were produced that day.
1 mark

Answer: 25 toys or 30 toys

Where the marks are

Takes the number of toys as $x$ and the cost per toy as $55 - x$ (½ mark)
Forms $x (55 - x) = 750$ (1 mark)
Gets $x^{2} - 55 x + 750 = 0$ (1 mark)
Factorises as $(x - 25) (x - 30) = 0$ (1½ marks)
Gets $x = 25$ or $30$ (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 430/2/1 (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 2024: question 32

Hints

Step-by-step solution

Revise the chapter

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