Case Study – 2 Sumant's mother started a new shoe shop. To display the shoes, she put 3 pairs of shoes in the 1st row, 5 pairs in the 2nd row, 7 pairs in the 3rd row and so on. (The page shows a 'New Collection Big Sale' social media advertisement for shoes.) Based on the above information, answer the following questions : (i) How many pairs of shoes are displayed in the 6th row ? (ii) What is the difference of pairs of shoes in the 1st row and the 6th row ? (iii) (a) Find the total number of pairs of shoes displayed in the first 15 rows. (iii) (b) If the pairs of shoes displayed in the 4th row are 'on sale' at price of ₹ 500 for each pair, then find the total amount (money) earned by Sumant's mother if all shoes displayed in the 4th row are sold out.

MathsCBSE Class 10 · Basic · Board exam 2024, set 430/5/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic 2024: question 37

Set in the CBSE Class 10 board exam of 2024, paper 430/5/1, section E, question 37, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q37 · 4 marks · Case-basedCompetency-basedArithmetic Progressions

Case Study – 2

Sumant's mother started a new shoe shop. To display the shoes, she put 3 pairs of shoes in the 1st row, 5 pairs in the 2nd row, 7 pairs in the 3rd row and so on.

(The page shows a 'New Collection Big Sale' social media advertisement for shoes.)

Based on the above information, answer the following questions :

(i)
How many pairs of shoes are displayed in the 6th row ?
1 mark
(ii)
What is the difference of pairs of shoes in the 1st row and the 6th row ?
1 mark
(iii)
(a) Find the total number of pairs of shoes displayed in the first 15 rows.
2 marks
OR
(iii)
(b) If the pairs of shoes displayed in the 4th row are 'on sale' at price of ₹ 500 for each pair, then find the total amount (money) earned by Sumant's mother if all shoes displayed in the 4th row are sold out.
2 marks

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/5/1.

Hints

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

Hint 1

Write down the number of pairs row by row and look at how much it increases each time.

Hint 2

It is an AP, so use $a_{n} = a + (n - 1) d$ for the number in a particular row.

Hint 3

For the total in the first 15 rows, use $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ .

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) The number of pairs in successive rows is 3, 5, 7, ... This is an AP with $a = 3$ and $d = 2$ .
½ mark
(i) $a_{6} = a + 5 d = 3 + 5 (2) = 13$ pairs.
½ mark
(ii) Difference $= a_{6} - a_{1} = 13 - 3 = 10$ pairs.
1 mark
(iii)(a) Use $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ with $n = 15$ : $S_{15} = \frac{15}{2} [2 (3) + 14 (2)]$
1 mark
(iii)(a) $= \frac{15}{2} \times 34 = 255$ pairs.
1 mark
(iii)(b) $a_{4} = a + 3 d = 3 + 3 (2) = 9$ pairs.
1 mark
(iii)(b) Money earned $= 9 \times ₹500 = ₹4500$
1 mark

Answer: (i) 13 pairs; (ii) 10; (iii)(a) 255 pairs; (iii)(b) ₹4500

Where the marks are

(i) Identifies $a = 3$ , $d = 2$ (½ mark)
(i) Finds $a_{6} = 13$ (½ mark)
(ii) Finds the difference 10 (1 mark)
(iii)(a) Correct substitution in $S_{15}$ (1 mark)
(iii)(a) Gets 255 (1 mark)
(iii)(b) Finds $a_{4} = 9$ (1 mark)
(iii)(b) Money earned ₹4500 (1 mark)

Revise the chapter

Chapter: Arithmetic Progressions (notes, formulas, where marks are lost and every past question)
Topic: Finding nth Term from the Sum of n Terms

Practise this chapterBoard-style questions from Arithmetic Progressions, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 430/5/1 (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 37

Hints

Step-by-step solution

Revise the chapter

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