PSA_LEVEL-UP_QNR9) 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?
Ans: Let us assume number of orders received everyday be ‘p’. And backlog be ‘b’. Also, assuming the number of orders cleared per day by any truck is ‘x’.
When he uses 7 trucks for 4 days,
the total number of orders cleared = 7*x*4 = 28x = 4p+b ———-(A)
When he uses 3 trucks for 10 days,
the total number of orders cleared = 3*x*10 = 30x = 10p+b ————(B)
(B) – (A) gives
b=30*3p – 10p= 80p= 80x/3
Now, when he uses m trucks for 5 days,
the total number of orders cleared = m*x*5
5mx = 5p+b
= 5x/3 + 80x/3
=> m= 17/3 = 5.66
Minimum number of trucks required =6. Option C.