A watch repairer fixes (6) watches in the first hour and (2) more watches each next hour. How many watches are fixed in (8) hours?
Answer and explanation
Correct answer: (104)
The numbers of watches repaired each hour form the AP \(6,8,10,\ldots\), where \(a=6\), \(d=2\), and \(n=8\). Therefore, \(S_8=\frac{8}{2}[2(6)+(8-1)(2)]=4(12+14)=104\). Hence, the correct answer is \(104\). Finding only the work done in the eighth hour would not give the total work. Exam tip: In AP word problems, use \(S_n\) for a total, not \(a_n\).
Frequently asked questions
What is the correct answer to this question?
(104)
Why is this the correct answer?
The numbers of watches repaired each hour form the AP \(6,8,10,\ldots\), where \(a=6\), \(d=2\), and \(n=8\). Therefore, \(S_8=\frac{8}{2}[2(6)+(8-1)(2)]=4(12+14)=104\). Hence, the correct answer is \(104\). Finding only the work done in the eighth hour would not give the total work. Exam tip: In AP word problems, use \(S_n\) for a total, not \(a_n\).
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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