average

Question

A certain no of trucks were required to transport 60 tons of iron from  company. However it was found that each truck could take 0.5 tons of cargo less and another 4 trucks were required. How many trucks were initially planned to use?

1)10

2)20

3)15

4)25

Answer 1

Let the initial number of trucks be $n$ and $x$ be the load carried by each truck.

$$\begin{equation} 0.5 \times n = 4x \label{622eq1} \end{equation}$$

$$\begin{equation} (n+4) \times x = 60 \label{622eq2} \end{equation}$$

From $\ref{622eq1}$ and $\ref{622eq2}$,

$$0.5 \times n = 4 \times \frac{60}{n+4} \\\implies n^2 + 4n -480 = 0 \\\implies (n+24)(n-20) = 480 \\\implies n = 20 (\because n \geq 0)$$