X 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?
Options:
(A) 30
(B) 35
(C) 40
(D) 45
Official Answer Key:
A
Step-by-Step Solution & Explanation
• Let b = work-rate of the X-bullock group and t = work-rate of the Y-tractor group (field/day, treating ‘X bullocks’ and ‘Y tractors’ as fixed groups).
• (Xb + Yt)×8 = 1 ⇒ Xb + Yt = 1/8.
• (0.5·Xb + 2·Yt)×5 = 1 ⇒ 0.5Xb + 2Yt = 1/5.
• From the first equation, Xb = 1/8 – Yt. Substituting: 0.5(1/8–Yt) + 2Yt = 1/5 ⇒ 1/16 + 1.5Yt = 1/5 ⇒ 1.5Yt = 1/5–1/16 = 11/80 ⇒ Yt = 11/120.
• Xb = 1/8 – 11/120 = 15/120 – 11/120 = 4/120 = 1/30.
• X bullocks alone complete the field at rate 1/30 field/day ⇒ time = 30 days.
• Final Answer: (A) 30
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.