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- Quantitative Aptitude
A person travels $\frac{1}{3}$ of his journey by bus at $60\, km / h$ , $\frac{1}{3}$ by scooter at $30\, km / h$ and the rest by walking at $10 \,km / h$. Find his average speed for the whole journey. (in $km/h$)
$30$
$33 \frac{1}{3}$
$20$
$50$
Solution
Let $'S'$ be the total distance travelled.
Time taken for $1^{st}$ $\frac{1}{3}$$^{rd}$ of journey $=\frac{S / 3}{60}=\frac{S}{180}$ hour.
Time taken for $2^{st}$ $\frac{1}{3}$$^{rd}$ of journey $=\frac{S / 3}{30}=\frac{S}{90}$ hour.
Time taken for $3^{st}$ $\frac{1}{3}$$^{rd}$ of journey $=\frac{S / 3}{10}=\frac{S}{30}$ hour.
Average speed $=\frac{\text { Total distance travelled }}{\text { Total time taken }}$
$=\frac{5}{\frac{S}{180}+\frac{S}{90}+\frac{S}{30}}$
$=\frac{5}{5\left(\frac{1}{180}+\frac{1}{90}+\frac{1}{30}\right)}$
$=\frac{180 \times 90 \times 30}{90 \times 30+180 \times 30+180 \times 90}$
$=\frac{180 \times 9 \times 3}{27+54+162}$
$=\frac{180}{1+2+6}$
$=20\, km / hr$
