Miller went to a Supermarket to buy vegetables. The cost of 5 kg tomatoes is $m$ whereas the cost of 4 kg potatoes is $n$ and 3 kg broccoli is $p$. How much money did he spend on buying $8$ kg tomatoes, $6$ kg potatoes and $4$ kg broccoli ?

The correct option is D $\frac{8m}{5}+\frac{6n}{4}+\frac{4p}{3}$
Cost of $5$ kg tomatoes is $m$.

Cost of $4$ kg potatoes is $n$.

Cost of $3$ kg broccoli is $p$.

So, the cost of $1$ Kg tomatoes = $\frac{m}{5}$

The cost of $1$ Kg potatoes = $\frac{n}{4}$

And, the cost of $1$ Kg broccoli = $\frac{p}{3}$


Miller bought $8$ Kg tomatoes, $6$ Kg potatoes and $4$ Kg broccoli.

Cost of $8$ Kg tomatoes = $8$ $\times$ cost of $1$ Kg tomatoes = $8\times \frac{m}{5}=\frac{8m}{5}\cdots \left(1\right)$

Cost of $6$ Kg potatoes = $6$ $\times$ cost of $1$ Kg potatoes = $6\times \frac{n}{4}=\frac{6n}{4}\cdots \left(2\right)$

Similarly, the cost of $4$ Kg broccoli = $4\times$ cost of $1$ Kg broccoli = $4\times \frac{p}{3}=\frac{4p}{3}\cdots \left(3\right)$

From $\left(1\right),\left(2\right)$ and $\left(3\right)$,

The cost of $8$ Kg tomatoes, $6$ Kg potatoes and $4$ broccoli = cost of $8$ Kg tomatoes + cost of $6$ Kg potatoes + cost of $4$ broccoli

So, the cost of $8$ Kg tomatoes, $6$ Kg potatoes and $4$ broccoli= $\frac{8m}{5}+\frac{6n}{4}+\frac{4p}{3}$

$\therefore$ Miller would have spent $\frac{8m}{5}+\frac{6n}{4}+\frac{4p}{3}$ money on buying the vegetables.