Question

If a bus travels 160km in 4 hours and a train travels 320km in 5 hours at uniform speed, then what is the ratio of distances travelled by them in one hour?
(A). $8:5$
(B). $5:8$
(C). $4:5$
(D). $1:2$

Answer 1

Hint: First, we will find distance travel in one hour using a unitary method in both bus and train. Then after getting the distance in one hour will take the ratio of bus to train distance and then we get our answer easily. Here, uniform speed is given so, ratio will be as ${\displaystyle \frac{\text{d1}}{\text{t1}}}={\displaystyle \frac{\text{d2}}{\text{t2}}}$ where speed parameter is constant.

Complete step-by-step solution -
Here, we are given distances travelled by bus and train is 160km and 320km in 4 hours and 5 hours, respectively. We need to find a distance ration of one hour.
So, we will use a unitary method for finding distance in one hour.
For bus:
$\begin{array}{rl}& 4hour=160km\\ & 1hour=?\end{array}$
$\therefore 1hour={\displaystyle \frac{160}{4}}=40km$ ……………………………..(1)
Now, for train:
$\begin{array}{rl}& 5hour=320km\\ & 1hour=?\end{array}$
$\therefore 1hour={\displaystyle \frac{320}{5}}=64km$ ………………………….(2)
So, now we will use speed distance formula which is given as
$\text{speed=}{\displaystyle \frac{\text{distance}}{\text{time}}}$
But here we are told that both bus and train are at uniform speed. So, no need to find value for speed.
Do, we can directly take ratio as
${\displaystyle \frac{\text{d1}}{\text{t1}}}={\displaystyle \frac{\text{d2}}{\text{t2}}}$ where d1 is distance of bus and d2 is distance of train.
But here t1 and t2 both are 1 hour so, the final ration will be
$\text{=}{\displaystyle \frac{\text{d1}}{\text{d}2}}$
$\text{=}{\displaystyle \frac{40}{64}}={\displaystyle \frac{5}{8}}$
Hence, option (b) is the correct answer.

Note: Another approach is to find the speed of the bus and train by using the formula $\text{speed=}{\displaystyle \frac{\text{distance}}{\text{time}}}$ . So, speed of bus $={\displaystyle \frac{160}{4}}=40{\displaystyle \frac{km}{hr}}$ and speed of train $={\displaystyle \frac{320}{4}}=64{\displaystyle \frac{km}{hr}}$ . So, in one-hour the bus travels $40{\displaystyle \frac{km}{hr}}$ and the train travels $64{\displaystyle \frac{km}{hr}}$ . So, the ratio will be $\text{=}{\displaystyle \frac{40}{64}}={\displaystyle \frac{5}{8}}$ . Do not take the ratio reversely that will lead to the answer $\text{=}{\displaystyle \frac{64}{40}}={\displaystyle \frac{8}{5}}$ which is the wrong answer. So, be careful while taking the ratio.