Maths · Algebra · chapter 5 of 14
Class 10 Maths Chapter 5: Arithmetic Progressions case study question with answers
One case-based question of the kind the board asks in Section E: a passage, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.
Case study · 4 marks
A caterer at a wedding hall in Indore stacks identical plastic cups one inside another. A single cup stands 11 cm tall, and each cup added to the stack raises its height by 1.5 cm, so stacks of 1, 2, 3, . . . cups are 11 cm, 12.5 cm, 14 cm, . . . tall. The cups are stored on shelves, and the caterer wants to know how tall different stacks will be and how many cups fit in a given height.
Part 1 · 1 mark
The height of a stack of 20 cups is
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Answer: (a) 39.5 cm
a₂₀ = 11 + 19 × 1.5 = 39.5 cm. (41 cm uses 20 steps of 1.5 cm.)
Part 2 · 1 mark
The number of cups in a stack 50 cm tall is
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Answer: (a) 27
11 + (n − 1) × 1.5 = 50 gives n − 1 = 26, n = 27. (33 divides 50 by 1.5.)
Part 3 · 2 marks
A shelf has 80 cm of clear height. Find the largest number of cups that can stand in one stack on it, and the height of that stack.
Answer and marking scheme
11 + 1.5(n − 1) ≤ 80 gives n − 1 ≤ 46, so n ≤ 47. The largest stack has 47 cups and is 11 + 46 × 1.5 = 80 cm tall, exactly filling the shelf.
- sets up 11 + 1.5(n − 1) ≤ 80 (1)
- 47 cups, 80 cm (1)
Or
A second kind of cup stands 9 cm tall alone, and each added cup raises its stack by 2 cm. For what number of cups are the two kinds of stack equally tall, and what is that height?
Answer and marking scheme
11 + 1.5(n − 1) = 9 + 2(n − 1) gives 2 = 0.5(n − 1), so n − 1 = 4 and n = 5. Height = 11 + 4 × 1.5 = 17 cm (and 9 + 4 × 2 = 17 cm).
- equates the two nth terms (1)
- 5 cups, 17 cm (1)