MathsCBSE Class 10 · Basic · Board exam 2024, set 430/4/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2024: question 35

Set in the CBSE Class 10 board exam of 2024, paper 430/4/1, section D, question 35, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q35 · 5 marks · Long answerCompetency-basedArithmetic Progressions

A manufacturer of TV sets produced 720 TV sets in the fourth year and 880 TV sets in the eighth year. Assuming that the production increases uniformly by a fixed number every year, find the production in the tenth year and the total production in the first seven years.

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

A uniform increase every year means the productions form an A.P. Write the 4th and 8th terms using $a_{n} = a + (n - 1) d$ .

Hint 2

Subtract the two equations to find $d$ , then find $a$ .

Hint 3

Use $a_{10} = a + 9 d$ and $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ with $n = 7$ .

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.

The production increases by a fixed number every year, so the yearly productions form an A.P. Let the first term be $a$ and the common difference be $d$ .
Fourth year: $a_{4} = a + 3 d = 720$ ...(i)
1 mark
Eighth year: $a_{8} = a + 7 d = 880$ ...(ii)
1 mark
Subtracting (i) from (ii): $4 d = 160$ , so $d = 40$ .
Substituting in (i): $a = 720 - 120 = 600$ .
1 mark
Production in the tenth year:
$a_{10} = a + 9 d = 600 + 9 \times 40 = 960$ TV sets.
1 mark
Total production in the first seven years:
$S_{7} = \frac{7}{2} [2 a + 6 d] = \frac{7}{2} [1200 + 240] = \frac{7}{2} \times 1440 = 5040$ TV sets.
1 mark

Answer: Tenth year: 960 TV sets; first seven years: 5040 TV sets

Where the marks are

Forms $a + 3 d = 720$ (1 mark)
Forms $a + 7 d = 880$ (1 mark)
Solves to get $d = 40$ and $a = 600$ (½ + ½ marks)
Finds $a_{10} = 960$ (1 mark)
Finds $S_{7} = 5040$ (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 430/4/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2024: question 35

Hints

Step-by-step solution

Revise the chapter

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