Question

A boy divided his total journey into 3 equal parts, with each part being \(x\) km. He travelled for a total time of one hour with speeds of \(y\) kmph, \(\frac{3y}{5}\) kmph, and \(\frac{2y}{5}\) kmph. Then \(x:y=\ ?\)

• A. \(6:1\)
• B. \(6:2\)
• C. \(6:3\)
• D. \(6:37\)

Hint:

When distances are equal, write time as \(\frac{\text{distance}}{\text{speed}}\) and add all time intervals.

Answer 1

The Correct Option is A

Step 1: Calculate time taken for each part. Distance of each part: \[ x \] Time for first part: \[ \frac{x}{y} \] Time for second part: \[ \frac{x}{3y/5} = \frac{5x}{3y} \] Time for third part: \[ \frac{x}{2y/5} = \frac{5x}{2y} \]

Step 2: Use total time = 1 hour. \[ \frac{x}{y} + \frac{5x}{3y} + \frac{5x}{2y} = 1 \] Taking \(\frac{x}{y}\) common: \[ \frac{x}{y} \left( 1+\frac53+\frac52 \right) = 1 \] \[ \frac{x}{y} \left( \frac6+\frac{10}6+\frac{15}6 \right) = 1 \] \[ \frac{x}{y} \cdot \frac{31}{6} = 1 \] \[ \frac{x}{y} = \frac6{31} \] Hence \[ x:y=6:31 \] The intended answer according to the options is \[ \boxed{6:31} \]