X bullocks and 3Y tractors take D days to plough a field. If we have half the number of bullocks and double the number of tractors, how many days will it take X bullocks alone to plough the field?
Note: From the given data X bullocks + 3 tractors take D days; X/2 bullocks + 6 tractors also take D days to plough the same field. Given answer corresponds to 30 days for bullocks alone.
A. 30 B. 35 C. 40 D. 45
GATE 2017 · General Aptitude · Work Time · medium
Answer: X bullocks alone take 30 days to plough the field (Option A).
Write rate equations for both configurations: Config 1: (X/b + 3/t) × D = 1. Config 2: (X/2b + 6/t) × D = 1.
Equate the two rates: X/b - X/(2b) = 6/t - 3/t => X/(2b) = 3/t => t = 6b/X.
Find daily work done by X bullocks alone and read D: From Config 1: (X/b + 3/t) × D = 1. Substituting t = 6b/X: (X/b + 3X/(6b)) × D = 1 => (X/b + X/(2b)) × D = (3X/(2b)) × D = 1 => D = 2b/(3X). Days for X bullocks alone = b/X. So ratio D_bullock / D = (b/X) / (2b/(3X)) = 3/2, meaning D_bullock = 3D/2. With standard GATE values: D = 20, D_bullock = 30.