Question

At a car park , 50% of the vehicles were cars , 30% were motorcycles and the rest of the 40 vehicles were vans .
1. Calculate the no. of motorcycles parked there .
2. If 40 cars left the car park , what percentage of the vehicles were parked there.

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{vehicles}\mathrm{be}\mathrm{x} \\ \mathrm{Then},50\%\mathrm{of}\mathrm{x}\mathrm{are}\mathrm{cars} \\ 30\%\mathrm{of}\mathrm{x}\mathrm{are}\mathrm{motorcycles} \\ \mathrm{So},\mathrm{rest}100-\left(50+30\right)=20\%\mathrm{are}\mathrm{vans} \\ \mathrm{Number}\mathrm{of}\hspace{0.17em}\mathrm{Vans}=40 \\ \mathrm{So},20\%\mathrm{of}\mathrm{x}=40 \\ \frac{20}{100}\times \mathrm{x}=40 \\ \mathrm{x}=\frac{40\times 100}{20} \\ \mathrm{x}=200 \\ \mathbf{So}\mathbf{,}\mathbf{}\mathbf{the}\mathbf{}\mathbf{number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{vehicles}\mathbf{}\mathbf{at}\mathbf{}\mathbf{the}\mathbf{}\mathbf{car}\mathbf{}\mathbf{park}\mathbf{}\mathbf{is}\mathbf{}\mathbf{200} \\ \mathrm{Number}\mathrm{of}\mathrm{cars}=\frac{50}{100}\times 200=100 \\ \mathrm{Number}\mathrm{of}\mathrm{motorcycles}=\frac{30}{100}\times 200=60 \\ \left(\mathbf{2}\right)40\mathrm{cars}\mathrm{left}\mathrm{the}\mathrm{park} \\ \mathrm{So},\mathrm{cars}\mathrm{left}\mathrm{in}\mathrm{car}\mathrm{park}=100-40=60 \\ \mathrm{So},\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{vehicles}\mathrm{left}=200-40=160 \\ \%\mathrm{age}\mathrm{of}\mathrm{vehicle}\mathrm{parked}=\frac{160}{200}\times 100=80\% \end{gathered}$$

Regards