A transporter receives the same number of orders each day. Currently, he has some pending orders (backlog) to be shipped. If he uses 4 trucks, then at the end of the 4th day he can clear all the orders. Alternatively, if he uses only 3 trucks, then all the orders are cleared at the end of the 5th day. What is the minimum number of trucks required so that there will be no pending order at the end of the 3rd day?
A. 20
B. 5
C. 6
D. 7
GATE 2011 · General Aptitude · Work Time · medium
Answer: Minimum trucks required = 6
Set up equations from given scenarios: Scenario 1: B + 4D = 4c * 4 = 16c. Scenario 2: B + 5D = 3c * 5 = 15c.
Solve for D and B: (B + 5D) - (B + 4D) = 15c - 16c => D = -c. Then B = 16c - 4D = 16c - 4(-c) = 20c.
Compute total orders to clear in 3 days: B + 3D = 20c + 3(-c) = 20c - 3c = 17c.
Find minimum trucks: n * c * 3 >= 17c => n * 3 >= 17 => n >= 17/3 = 5.67. Minimum integer n = 6. Check: 5 trucks: 5*3=15 < 17 (fails). 6 trucks: 6*3=18 >= 17 (works).