Project ForgeX bullocks and Y tractors take 8 days to plough a field. If we halve the number of bullocks and double the number of tractors, it takes 5 days to plough the same field. How many days will it take X bullocks alone to plough the field?
- 30
- B35
- C40
- D45
Explanation
Let 'Xb' be the combined daily work rate of all X bullocks and 'Yt' the combined rate of all Y tractors (as fractions of the field per day). Equation 1: (Xb+Yt)*8=1, so Xb+Yt=1/8. Equation 2: (Xb/2+2Yt)*5=1, so Xb/2+2Yt=1/5. From eq.1, Yt=1/8-Xb; substituting into eq.2: Xb/2+2(1/8-Xb)=1/5, giving Xb/2+1/4-2Xb=1/5, so -1.5*Xb=1/5-1/4=-1/20, giving Xb=1/30. So X bullocks alone take 30 days.
Source: GATE ME 2017 Session 2 (ME-2) (2017)
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