MathsCBSE Class 10 · Standard · Board exam 2023, set 30/6/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2023: question 36

Set in the CBSE Class 10 board exam of 2023, paper 30/6/1, section E, question 36, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q36 · 4 marks · Case-basedCompetency-basedPair of Linear Equations in Two Variables

A coaching institute of Mathematics conducts classes in two batches I and II and fees for rich and poor children are different. In batch I, there are 20 poor and 5 rich children, whereas in batch II, there are 5 poor and 25 rich children. The total monthly collection of fees from batch I is ₹ 9000 and from batch II is ₹ 26,000. Assume that each poor child pays ₹ x per month and each rich child pays ₹ y per month.

[Photograph of a classroom with students seated in rows facing a lecture/presentation screen.]

Based on the above information, answer the following questions:

(i)
Represent the information given above in terms of x and y.
1 mark
(ii)
Find the monthly fee paid by a poor child.
2 marks
OR
(ii)
Find the difference in the monthly fee paid by a poor child and a rich child.
2 marks
(iii)
If there are 10 poor and 20 rich children in batch II, what is the total monthly collection of fees from batch II?
1 mark

Figure in the paper: Photograph of a classroom: an audience of students seated in rows, facing a front presentation screen, with framed pictures on the side walls. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/6/1.

Hints

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

Hint 1

The total fee of a batch = (number of poor × x) + (number of rich × y).

Hint 2

Divide each equation by 5 to simplify it, then use substitution or elimination.

Hint 3

Once x and y are known, substitute the new numbers of children.

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.

(i) Batch I has 20 poor and 5 rich children, so $20 x + 5 y = 9000$ , i.e. $4 x + y = 1800$ .
Batch II has 5 poor and 25 rich children, so $5 x + 25 y = 26000$ , i.e. $x + 5 y = 5200$ .
1 mark
(ii) From $4 x + y = 1800$ we get $y = 1800 - 4 x$ .
Substituting in $x + 5 y = 5200$ : $x + 5 (1800 - 4 x) = 5200$ , so $9000 - 19 x = 5200$ .
This gives $19 x = 3800$ , so $x = 200$ .
1½ marks
(ii) The monthly fee paid by a poor child is ₹ 200.
½ mark
(ii) OR: Solve as above to get $x = 200$ . Then $y = 1800 - 4 (200) = 1000$ .
1½ marks
(ii) OR: Difference in monthly fee $= y - x = 1000 - 200 =$ ₹ 800.
½ mark
(iii) Total collection $= 10 x + 20 y = 10 (200) + 20 (1000) = 2000 + 20000 =$ ₹ 22000.
1 mark

Answer: (i) 20x + 5y = 9000, 5x + 25y = 26000; (ii) ₹ 200 OR difference ₹ 800; (iii) ₹ 22000

Where the marks are

Writes both equations $20 x + 5 y = 9000$ and $5 x + 25 y = 26000$ (1 mark)
Solves the pair correctly to get $x = 200$ (1½ marks)
States the poor child's fee as ₹ 200 (½ mark)
OR part: obtains $x = 200$ and $y = 1000$ (1½ marks)
OR part: difference ₹ 800 (½ mark)
Computes $10 x + 20 y =$ ₹ 22000 (1 mark)

Revise the chapter

Chapter: Pair of Linear Equations in Two Variables (notes, formulas, where marks are lost and every past question)
Topic: Word Problems on Linear Equations

Practise this chapterBoard-style questions from Pair of Linear Equations in Two Variables, one at a time, marked against the answer key and marking points.Back to the full paper2023 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.

CBSE Class 10 Mathematics Standard 2023: question 36

Hints

Step-by-step solution

Revise the chapter

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