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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 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? Correct Answer 6

 Concept:

The transporter receives the same number of order each day and he currently has pending orders.

Let 'x' be the number of daily orders and 'y' be the number of pending orders.

Calculation:

Given:

Condition I:

Use of 7 trucks each day finishes all orders in 4 days.

∴ total numbers of trucks used = 7 + 7 + 7 + 7 ⇒ 28.

Total orders received in 4 days = 4x.

Pending orders = y.

∴ 4x + y = 28      eq(1).

Condition II:

Use of 3 trucks each day finishes all orders in 10 days.

∴ total numbers of trucks used = 3 × 10 ⇒ 30.

Total orders received in 10 days = 10x.

Pending orders = y.

∴ 10x + y = 30      eq(2).

Solving eq (1) and eq (2).

x = 0.33 ⇒ Daily orders

y = 26.66 ⇒ Pending orders.

Condition III:

Use of 'n' trucks each day finishes all orders in 5 days.

∴ total numbers of trucks used = 5 × n ⇒ 5n.

Total orders received in 5 days = 5x.

Pending orders = y.

∴ 5x + y = 5n   

∴ (5 × 0.33)  + (26.66) = 5n

∴ n = 5.66 ≈ 6

∴ minimum 6 number of trucks required so that there will be no pending order at the end of the 5th day.

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