GATE | GATE CS 2011 | Question 64

A 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?

(A) 4
(B) 5
(C) 6
(D) 7


Answer: (C)

Explanation:

Let each truck can take at most x units.  Let the daily order be y and let backlog be z.

7*4*x = 4y + z
3*10*x = 10y + z

We need value of (5y + z)/5 in terms of x.

We can get value of y by subtracting first from second
6y = 2x
y = x/3

We can get value of z by substituting  value of y in first equation
4y + z = 28x
4(x/3) + z = 28x
z = (80/3)x

So the value of (5y + z)/5 is 5*(x/3) + (80/3)x  which is 17/3

So almost 6 trucks needed.

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