UPSC Prelims 2007 · General Studies
Question 145: Basic Numeracy
A and B can complete work together in 5 days. If A works at twice his speed and B at half of his speed, this work can be finished in 4 days. How many days would it take for A alone to complete the job?
AnswerThe answer is (a).
Let A's one-day work be x and B's be y. Together, x + y = 1/5. With A at double speed and B at half speed, 2x + y/2 = 1/4, which is 4x + y = 1/2. Subtract the first equation: 3x = 1/2 - 1/5 = 3/10, so x = 1/10. A alone takes 10 days.
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) Correct: x = 1/10 gives 10 days.
- (b) 12 days gives x = 1/12, which does not fit the equations.
- (c) 15 days gives x = 1/15, which does not fit the equations.
- (d) 18 days gives x = 1/18, which does not fit the equations.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2007, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.