Project ForgeA transporter receives the same number of orders each day. Currently, he has some pending orders (backlog) to be shipped. If he uses 7 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 10th day. What is the minimum number of trucks required so that there will be no pending order at the end of the 5th day?
- A4
- B5
- 6
- D7
Explanation
Let backlog=b, new orders/day=r, one truck's clearance rate/day=c. With 7 trucks clearing by day 4: 28c = b+4r. With 3 trucks clearing by day 10: 30c = b+10r. Subtracting: 2c = 6r, so c=3r. Substituting back: 28(3r)=b+4r gives b=80r. To clear by day 5 with n trucks: 5nc >= b+5r, i.e. 15nr >= 85r, so n >= 85/15 = 5.67, meaning n=6 is the minimum integer number of trucks.
Source: GATE ME 2011 (2011)
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