Question

A person travelled 80 km in 6 hours. If the person travelled the first part with a uniform speed of 10 kmph and the remaining part with a uniform speed of 18 kmph. What percentage of the total distance is travelled at a uniform speed of 10 kmph?

• A. 28.25
• B. 37.25
• C. 43.75
• D. 50.00

Hint:

To solve such problems, break the total time into two parts based on the distances travelled at different speeds, then use the time equation to find the distance.

Answer 1

The Correct Option is C

Let the distance travelled at 10 kmph be \( x \) km.
Then, the time taken to travel \( x \) km is: \[ \frac{x}{10}. \]
The remaining distance, travelled at 18 kmph, will be \( (80 - x) \) km. The time taken to travel this distance is: \[ \frac{80 - x}{18}. \]
The total time taken is 6 hours. Therefore, we have the equation: \[ \frac{x}{10} + \frac{80 - x}{18} = 6. \]
Multiplying through by 90 (the least common multiple of 10 and 18) to eliminate the denominators: \[ 9x + 5(80 - x) = 540. \]
Expanding and solving for \( x \): \[ 9x + 400 - 5x = 540, \] \[ 4x = 140, \] \[ x = 35. \]
So, the person travelled 35 km at 10 kmph. The percentage of the total distance travelled at 10 kmph is: \[ \frac{35}{80} \times 100 = 43.75%. \]
Thus, the correct answer is (C) 43.75.