CBSE Class 10 Maths (Basic) 2025 · Paper 430/5/1 · Question 38

Arithmetic Progressions 4 marks Medium

A tent house owner provides furniture on rent. He stacks chairs in his shop to save space. In the diagram, the height of seat of chair from ground is represented by

h_{1}, h_{2}, h_{3}, h_{4}, \dots

The height of first seat is 44 cm from ground level and gap between every two seats is 10 cm.

Stack of chairs schematic

(i)Write the values of $h_{1}, h_{2}, h_{3}, h_{4}$ and $h_{5}$ in this order only.[1]
(ii)Show that the above values form an A.P. Write its first term and common difference.[1]
(iii)(a)If chairs can be stacked up to the maximum height of 160 cm, then find the maximum number of chairs in a stack.[2]
(iii)(b)OR Is it possible to stack 15 chairs if maximum height of the stack can not be more than 180 cm? Justify your answer.[2]

Answer

(i)

h_{1} = 44

cm,

h_{2} = 54

cm,

h_{3} = 64

cm,

h_{4} = 74

cm,

h_{5} = 84

cm; (ii) Each height is

10

cm more than the one before it, so the heights form an A.P. with first term

a = 44

cm and common difference

d = 10

cm; (iii)(a) At most

12

chairs can be stacked; (iii)(b) No, it is not possible: the

15

th seat would be at

h_{15} = 184

cm, which is more than

180

cm.

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CBSE Class 10 Maths (Basic) 2025 · Paper 430/5/1, Question 38 — all 38 questions with answers →

CBSE Class 10 Maths (Basic) 2025 · Paper 430/5/1 · Question 38

Answer

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