Subject: General Aptitude · Chapter: Time and Distance · Exam: · Marks: · Difficulty:
A man performs 2/15 of the total journey by rail, 9/20 by bus and the remaining 10 km, on the cycle. His total journey is [UPSSSC-Lower Subordinate (Pre.) Exam, 2016]
(a)31.2 km
(b)38.4 km
(c)32.8 km
(d)24 km
Answer
Answer (as printed): D
Explanation
Let total distance covered by man be $x \mathrm{km}$ Journey covered by rail $=\frac{2 x}{15}$ Journey covered by bus $=\frac{9 x}{20}$ Remaining covered by Cycle $=10 \mathrm{km}$ $$\therefore \quad x\left(1-\frac{2}{15}-\frac{9}{20}\right)=10$$ LCM of 15 and 20 = 60 $$\begin{aligned} & x\left(\frac{60-8-27}{60}\right)=10 \\ & \Rightarrow x\left(\frac{25}{60}\right)=10 \\ & x=\frac{10 \times 60}{25}=24 \mathrm{km} . \end{aligned}$$