Case Study – 3 Deepankar bought 3 notebooks and 2 pens for ₹ 80 and his friend Suryansh bought 4 notebooks and 3 pens for ₹ 110 from the school bookshop. Based on the above information, answer the following questions. (i) If the price of one notebook be ₹ x and the price of one pen be ₹ y, write the given situation algebraically. (ii)(a) What is the price of one notebook ? (ii)(b) What is the price of one pen ? (iii) What is the total amount to be paid by Suryansh, if he purchases 6 notebooks and 3 pens ?

MathsCBSE Class 10 · Basic · Board exam 2024, set 430/4/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic 2024: question 38

Set in the CBSE Class 10 board exam of 2024, paper 430/4/1, section E, question 38, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q38 · 4 marks · Case-basedCompetency-basedPair of Linear Equations in Two Variables

Case Study – 3

Deepankar bought 3 notebooks and 2 pens for ₹ 80 and his friend Suryansh bought 4 notebooks and 3 pens for ₹ 110 from the school bookshop.

Based on the above information, answer the following questions.

(i)
If the price of one notebook be ₹ x and the price of one pen be ₹ y, write the given situation algebraically.
1 mark
(ii)(a)
What is the price of one notebook ?
2 marks
OR
(ii)(b)
What is the price of one pen ?
2 marks
(iii)
What is the total amount to be paid by Suryansh, if he purchases 6 notebooks and 3 pens ?
1 mark

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/4/1.

Hints

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

Hint 1

Write one equation for each person: number of notebooks × x + number of pens × y = amount paid.

Hint 2

Use elimination: make the coefficients of one variable equal in both equations, then subtract.

Hint 3

Once you know x and y, the amount for 6 notebooks and 3 pens is $6 x + 3 y$ .

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) Deepankar: $3 x + 2 y = 80$ ...(1)
½ mark
Suryansh: $4 x + 3 y = 110$ ...(2)
½ mark
(ii)(a) Multiply (1) by 3 and (2) by 2:
$9 x + 6 y = 240$ and $8 x + 6 y = 220$
1 mark
Subtracting the second from the first gives $x = 20$ .
The price of one notebook is ₹ 20.
1 mark
(ii)(b) Multiply (1) by 4 and (2) by 3:
$12 x + 8 y = 320$ and $12 x + 9 y = 330$
1 mark
Subtracting the first from the second gives $y = 10$ .
The price of one pen is ₹ 10.
1 mark
(iii) Amount for 6 notebooks and 3 pens $= 6 \times 20 + 3 \times 10 = 120 + 30 = ₹ 150$
1 mark

Answer: (i) $3 x + 2 y = 80$ , $4 x + 3 y = 110$ ; (ii)(a) ₹ 20; (ii)(b) ₹ 10; (iii) ₹ 150

Where the marks are

(i) Writes $3 x + 2 y = 80$ (½ mark)
(i) Writes $4 x + 3 y = 110$ (½ mark)
(ii)(a) Solves the pair of equations correctly to get x = 20 (2 marks)
(ii)(b) Solves the pair of equations correctly to get y = 10 (2 marks)
(iii) Total amount = ₹ 150 (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 paper2024 board paper, set 430/4/1 (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 38

Hints

Step-by-step solution

Revise the chapter

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