GATE CSE 2011 | Question: 64

Question

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 $4^{th}$ 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 $10^{th}$ day. What is the minimum number of trucks required so that there will be no pending order at the end of $5^{th}$ day?

• A. $4$
• B. $5$
• C. $6$
• D. $7$

Comments

Let X is the number of trucks that can clear the order in 5^th day.

he uses only 3 trucks, then all the orders are cleared at the end of the 10th day.

1 truck can clear the order in 30days

1 day work by 1 truck = 1 / 30 work

What is the minimum number of trucks required so that there will be no pending order at the end of 5th day?

5 day work by 1 truck = 5 / 30 = 1/6 work

5 day work by X trucks = X/6 work

So, X has to be 6.

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7 trucks then at the end of 4^th day it will clear all the order.

so by using 1 truck it will clear the order in 28 days as less the number of truck more number of days require to clear the order.

by using 3 trucks it will clear order in ceil(28/3)=10 days

we have to find how many trucks will clear the order at the end of 5^th day

option A->ceil(28/4)=7 days 

option B->ceil(28/5)=6 days

option D->ceil(28/7)=4 days

option C->ceil(28/6)=5 days

so option c is the answer

Answer 1

$\frac{T_{1}}{T_{2}}=\frac{D_{1}}{D_{2}}$

T = trucks & D= days.

so, $\frac{3}{T_{2}}=\frac{5}{10}$

6 trucks are required

Comments

wrong approach