Question : A takes 2 hours 30 minutes more than B to walk 40 km. If A doubles his speed, then he can make it in 1 hour less than B. How much time (in hours) does A require for walking a 40 km distance?
Option 1: 6
Option 2: 7
Option 3: 9
Option 4: 5
Correct Answer: 7
Solution :
Let the speed of A be $x$ km/hr.
Time taken by A = $\frac{40}{x}$ hr
Time taken by B = $\frac{40}{x}-2.5$ hr
When speed of A = $2x$,
Time taken by A = $\frac{40}{2x}$
According to the question,
$(\frac{40}{x}-2.5) - (\frac{40}{2x}) = 1$
⇒ $\frac{40}{x}-\frac{40}{2x} = 3.5$
⇒ $\frac{40}{2x} = 3.5$
$\therefore x = \frac{40}{7}$
Time taken by A = $\frac{40}{\frac{40}{7}}$ = 7 hours
Hence, the correct answer is 7.
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