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:

• A. 50, 15
• B. 30, 40
• C. 30, 20
• D. 40, 30

Answer 1

The correct option is A 50, 15

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,
$10=100a+120b....\left(3\right)$
$16=200a+180b....\left(4\right)$
Multiplying (3) with 2, we get,
$20=200a+240b....\left(5\right)$
$\left(5\right)-\left(4\right)$, we get,
$4=60b$
$\Rightarrow b=\frac{1}{15}$
Substituting b in (3), we get,
$10=100a+\frac{120}{15}$
$\Rightarrow a=\frac{1}{50}$
$\because a=\frac{1}{x}\Rightarrow x=50$ kmph
$\because b=\frac{1}{b}\Rightarrow y=15$ kmph
$\therefore$ Speed of the bike $=50$ kmph
Speed of the car $=15$ kmph