MathsCBSE Class 10 · Basic · Sample paper, session 2023-24 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic sample paper 2023-24: question 28(a)

From the official CBSE sample question paper for 2023-24, section C, question 28(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28(a) · 3 marks · Short answerCompetency-basedPair of Linear Equations in Two Variables

The coach of a cricket team buys 4 bats and 1 ball for Rs. 2050. Later, she buys 3 bats and 2 balls for Rs. 1600. Find the cost of each bat and each ball.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

Let the bat cost Rs x and the ball Rs y. Write one equation for each purchase.

Hint 2

From the first equation, $y = 2050 - 4 x$ . Substitute this into the second equation.

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 cost of one bat be Rs $x$ and the cost of one ball be Rs $y$ .
½ mark
$4 x + y = 2050$ ...(1)
$3 x + 2 y = 1600$ ...(2)
½ mark
From (1), $y = 2050 - 4 x$ .
½ mark
Substituting in (2): $3 x + 2 (2050 - 4 x) = 1600 \Rightarrow 3 x + 4100 - 8 x = 1600 \Rightarrow - 5 x = - 2500 \Rightarrow x = 500$
½ mark
Substituting in (1): $y = 2050 - 4 (500) = 2050 - 2000 = 50$
½ mark
Cost of one bat = Rs 500; cost of one ball = Rs 50.
½ mark

Answer: Bat = Rs 500, Ball = Rs 50

Where the marks are

Defines the variables (1/2 mark)
Forms both equations (1/2 mark)
Expresses $y$ in terms of $x$ (1/2 mark)
Finds $x = 500$ (1/2 mark)
Finds $y = 50$ (1/2 mark)
States the costs (1/2 mark)

Revise the chapter

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

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 paperSample paper 2023-24 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2023-24: question 28(a)

Hints

Step-by-step solution

Revise the chapter

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