UPSC Prelims 2002 · General Studies
Question 104: Basic Numeracy
Amit started a business by investing Rs 30,000. Rahul joined the business after some time and invested Rs 20,000. At the end of the year, profit was divided in the ratio of 2 : 1. After how many months did Rahul join the business?
AnswerThe answer is (b).
Amit's capital works for 12 months: 30,000 x 12 = 3,60,000 rupee-months. If Rahul joins x months late, his 20,000 works for 12 - x months. Profit is shared in the ratio of capital times time, 2 : 1, so 3,60,000 : 20,000(12 - x) = 2 : 1. That gives 20,000(12 - x) = 1,80,000, so 12 - x = 9 and x = 3 months.
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) 2 months gives Rahul 10 months and a ratio of 360 : 200, not 2 : 1.
- (b) Right: 3 months late leaves 9 months of 20,000, a 2 : 1 ratio.
- (c) 4 months gives 8 months and a ratio of 360 : 160, not 2 : 1.
- (d) 5 months gives 7 months and a ratio of 360 : 140, not 2 : 1.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2002, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.