At the first stop on his route- a driver unloaded 2-5 of the packages in his van- After he unloaded another 3 packages- at his next step 1-2 of the original number of packages remained- How many packages were in the van before the first delivery-

The correct option is B 30 Let x be the original number of packages in the van.Then x2(total #160; unloaded packages) #160; = #160; 2x5(u ...

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Standard XII

Mathematics

Properties of Set Operation

At the first ...

Question

At the first stop on his route, a driver unloaded $\frac{2}{5}$ of the packages in his van. After he unloaded another $3$ packages, at his next step $\frac{1}{2}$ of the original number of packages remained. How many packages were in the van before the first delivery?

25

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30

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Solution

The correct option is B $30$
Let $x$ be the original number of packages in the van.
Then $\frac{x}{2} (t o t a l u n l o a d e d p a c k a g e s) = \frac{2 x}{5} (u n l o a d e d p a c k a g e s a t f i r s t s t e p) + 3$
$\Rightarrow \frac{5 x - 4 x}{10} = 3$
$\Rightarrow x = 30$

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At the first stop on his route, a driver unloaded 25 of the packages in his van. After he unloaded another 3 packages, at his next step 12 of the original number of packages remained. How many packages were in the van before the first delivery?

The correct option is B 30Let x be the original number of packages in the van.Then x2(totalunloadedpackages)=2x5(unloadedpackagesatfirststep)+3⇒5x−4x10=3⇒x=30

At the first stop on his route, a driver unloaded $\frac{2}{5}$ of the packages in his van. After he unloaded another $3$ packages, at his next step $\frac{1}{2}$ of the original number of packages remained. How many packages were in the van before the first delivery?

The correct option is B $30$
Let $x$ be the original number of packages in the van.
Then $\frac{x}{2} (t o t a l u n l o a d e d p a c k a g e s) = \frac{2 x}{5} (u n l o a d e d p a c k a g e s a t f i r s t s t e p) + 3$
$\Rightarrow \frac{5 x - 4 x}{10} = 3$
$\Rightarrow x = 30$