A man performs \(\displaystyle\frac{2}{15}\) of the total journey by rail, \(\displaystyle\frac{9}{20}\) by bus and the remaining 10 km on a cycle. His total journey is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 24 km
Rail and bus together cover a fraction of the journey; the rest of the journey is the 10 km on the cycle, so finding that fraction gives the whole.
Rail and bus: \(\displaystyle\frac{2}{15}+\frac{9}{20}=\frac{8+27}{60}=\frac{35}{60}=\frac{7}{12}\)
Cycle: \(1-\displaystyle\frac{7}{12}=\frac{5}{12}\) of the journey, which is 10 km
Total journey \(=10\times\displaystyle\frac{12}{5}=24\) km