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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 $4^{th}$ 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?

1. $4$
2. $5$
3. $6$
4. $7$
edited | 2.6k views

Let the amount of orders received per day be $x,$ the amount of pending orders be $y$ and the amount of orders carried by a truck each day be $z.$

$7z \times 4 = 4x + y \quad \to (1)$

$3z \times 10 = 10x + y\quad \to (2)$

$(2) - (1) \implies 2z = 6x, z = 3x, y = 80x$

We want to find the number of trucks to finish the orders in $5$ days. Let it be A.

$Az \times 5 = 5x + y$

$15Ax = 5x + 80x$

$A = \lceil85/15\rceil = \lceil17/3\rceil = 6$

So, minimum $6$ trucks must be used.
edited by
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Total product to be shipped at the end of 4th day = 4x + y

this product is divided into 7 trucks and it takes 4days.

So, $\frac{4x+y}{7} = 4$

Is this way of thinking is wrong?? (seems similar to yours)
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actually you are doing the same thing . In above @arjun sir take z as no of order to carried by each truck in each day this z u have taken as 1 since it will not matter as you can assume any value.since answer will  come independent to no of order.

Say, amount of order is x

7 truck 4 days can clear the order x

1   "    4   "         "     "     "    "     x/7

1   "    1   "           "    "    "     "        x/28.........................(i)

Similarly,

3  truck  in 10 days can clear the order x

1  "        "    1   "      "     "       "   "     x/30..........................(ii)

(i) and (ii) equations are equivalent

So, x/28 $\alpha$ x/30

x/28 = c. x/30

or, c=15/14

4 days x work is done by 7 trucks

1   "    x  "      "    "     "   7*4  "

5   "    x   "    "     "     "   7*4 /5 "

and it is equivalent to previous task , i.e. 7*4 /5 c = 7*4 /5 * 15/14 = 6 days
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u r wrong in the last four lines
c is the ans
answered by Loyal (5.3k points) 1 flag:
✌ Edit necessary (syncronizing “explain it”)

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