Question

A person travels a distance of 100 km by bike and 120 km by car in a span of 10 hrs. He then travels 200 km by bike and 180 km by car in a span of 16 hrs. The speed of bike and car, respectively, in kmph is:

[1 mark]

• A. 30, 20
• B. 20, 30
• C. 30, 40
• D. 40, 30

Answer 1

The correct option is B 20, 30

Let the speed of the bike $=x$
speed of car $=y$
$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$
In the first case, the time taken to travel by bike $=\frac{100}{x}hr$
The time taken to travel by car $=\frac{120}{y}hr$
Total time $=$ Time taken to travel by bike $+$ car
$10=\frac{100}{x}+\frac{120}{y}...\left(1\right)$
Similarly, in the second case,
$16=\frac{200}{x}+\frac{180}{y}....\left(2\right)$
Now, by assuming $\frac{1}{x}=a$ and $\frac{1}{y}=b$, wee get,
$10=100a+150b....\left(3\right)$
$16=200a+18b....\left(4\right)$
Multiplying (3) with 2, we get,
$20=200a+300b....\left(5\right)$
$\left(5\right)-\left(4\right)$, we get,
$4=120b$
$\Rightarrow b=\frac{1}{30}$
Substituting b in (3), we get,
$10=100a+\frac{150}{30}$
$\Rightarrow a=\frac{1}{20}$
$\because a=\frac{1}{x}\Rightarrow x=20$ kmph
$\because b=\frac{1}{b}\Rightarrow y=30$ kmph
$\therefore$ Speed of the bike $=20$ kmph
Speed of the car $=30$ kmph