In a building the first floor has 150 windows and each next floor has 10 fewer windows. Which floor will have 60 windows?
Answer and explanation
Correct answer: 10
This is an arithmetic-progression word problem involving the nth term. The first floor has a = 150 windows and each succeeding floor has 10 fewer, so the common difference is d = −10. For the nth floor, aₙ = a + (n−1)d. Substituting the required number gives 60 = 150 + (n−1)(−10). Hence −90 = −10(n−1), so n−1 = 9 and n = 10. Therefore option C is correct. The sequence is 150, 140, 130, ..., 60, and 60 is the tenth term. The other choices correspond to different window counts.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
This is an arithmetic-progression word problem involving the nth term. The first floor has a = 150 windows and each succeeding floor has 10 fewer, so the common difference is d = −10. For the nth floor, aₙ = a + (n−1)d. Substituting the required number gives 60 = 150 + (n−1)(−10). Hence −90 = −10(n−1), so n−1 = 9 and n = 10. Therefore option C is correct. The sequence is 150, 140, 130, ..., 60, and 60 is the tenth term. The other choices correspond to different window counts.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Word problems based on APs.
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