UPSC Prelims 2008 · General Studies
Question 4: Basic Numeracy
Carpenter A can make a chair in 6 hours, carpenter B in 7 hours and carpenter C in 8 hours. If each carpenter works for 8 hours per day, how many chairs will be made in 21 days?
AnswerThe answer is (c).
Work in rates. Per hour the three carpenters make 1/6 + 1/7 + 1/8 chairs. The common denominator is 168, so the sum is (28 + 24 + 21)/168 = 73/168 chairs per hour. Working 8 hours a day for 21 days is 168 hours, so together they make 168 x 73/168 = 73 chairs.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
This follows an unofficial answer: UPSC has not published its key for this year, and if that answer is wrong, so is this path.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) 61 is too low; the combined rate over 168 hours gives 73.
- (b) 67 is too low; adding the three rates over 168 hours gives 73, not 67.
- (c) Combined rate 73/168 chairs per hour times 168 hours is 73 chairs.
- (d) 79 is too high; it needs a faster combined rate than 73/168 per hour.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2008, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.