Maths · Algebra · chapter 5 of 14

Class 11 Maths Chapter 5: Linear Inequalities case study question with answers

One case-based question of the kind CBSE-pattern school exams ask: 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 school in Bhopal is printing copies of its annual magazine and has ₹ 15000 for the job. Printer P charges ₹ 3000 to set up and ₹ 40 for each copy. Printer Q charges ₹ 1200 to set up and ₹ 55 for each copy. The school will order n copies, where n is a whole number, from one printer only. Before choosing, the coordinator writes the cost of each printer as an expression in n and compares the two, keeping the budget in mind.
Part 1 · 1 mark
Printer P is cheaper than Printer Q exactly when
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Answer: (c) n > 120

3000 + 40n < 1200 + 55n gives 1800 < 15n, so n > 120.

Part 2 · 1 mark
The greatest number of copies the school can order from Printer P within its budget is
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Answer: (d) 300

3000 + 40n ≤ 15000 gives 40n ≤ 12000, n ≤ 300. Exactly ₹ 15000 is allowed, so 300. 375 ignores the set-up charge.

Part 3 · 2 marks
Find all the numbers of copies for which Printer P is both cheaper than Printer Q and within the budget. Write the answer as a double inequality and state how many such numbers there are.
Answer and marking scheme

P cheaper: n > 120. Within budget: n ≤ 300. Both: 120 < n ≤ 300, n a whole number, i.e. n = 121, 122, …, 300: 180 numbers.

  • combines n > 120 and n ≤ 300 into 120 < n ≤ 300 (1)
  • 180 numbers (1)
Or
Find the greatest number of copies the school can order from Printer Q within its budget, and say which printer is cheaper for that number of copies.
Answer and marking scheme

1200 + 55n ≤ 15000 gives 55n ≤ 13800, n ≤ 250 10/11, so 250 copies. For n = 250, P costs 3000 + 10000 = ₹ 13000 and Q costs 1200 + 13750 = ₹ 14950, so P is cheaper (as 250 > 120).

  • 55n ≤ 13800 gives 250 copies (1)
  • compares costs: P cheaper (1)
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