Question

A man wants to reach a certain destination. One sixth of the total distance is muddy while half the distance is tar road. For the remaining distance he takes a boat. His speed of traveling in mud, in water & on tar road is in the ratio 3 : 4 : 5. The ratio of the durations he requires to cross the patch of mud stream and tar road is :

• A. $\frac{1}{2}:\frac{4}{5}:\frac{5}{2}$
• B. $3:8:15$
• C. $10:15:18$
• D. $1:2:3$

Answer 1

Answer: (C)

$10:15:18$

Ratio of speeds are

$v_1:v_2:v_3=3:4:5$

Let total distance be $D$

Ratio of time duration will be

$t_1:t_2:t_3=\frac{\frac{D}{6}}{3}:\frac{\frac{D}{3}}{4}:\frac{\frac{D}{2}}{5}$

$t_1:t_2:t_3=\frac{1}{18}:\frac{1}{12}:\frac{1}{10}$

Multiplying $RHS$ by $180$ which is LCM of $18,12,10$

$t_1:t_2:t_3=10:15:18$

Therefore Answer is $\left(C\right)$