Arithmetic

Time, Speed & Distance

Medium

applied

In a 500 metres race, the ratio of speeds of two participants Meena and Kamal is 4:5 respectively. If Meena has a start of 200 metres, find the distance by which Meena wins.

375 metres

125 metres

150 metres

300 metres

✅ Correct Option: 2

The race distance is 500 metres. The speed ratio of Meena to Kamal is 4:5. Meena has a head start of 200 metres.

Since Meena starts 200m ahead, the distance she needs to cover is:

$500 - 200 = 300$ metres

Kamal starts from the beginning and needs to cover the full 500 metres.

Let Meena's speed be $4x$ m/unit time and Kamal's speed be $5x$ m/unit time, where $x$ is a constant.

Time taken by Meena to finish the race:

$\text{Time} = \dfrac{\text{Distance}}{\text{Speed}}$

$\text{Time} = \dfrac{300}{4x}$

$\text{Time} = \dfrac{75}{x}$ units

When Meena finishes, Kamal has been running for the same time of $\dfrac{75}{x}$ units.

Distance covered by Kamal in this time:

$\text{Distance} = \text{Speed} \times \text{Time}$

$\text{Distance} = 5x \times \dfrac{75}{x}$

$\text{Distance} = 375$ metres

When Meena crosses the finish line at 500 metres, Kamal is at 375 metres.

Distance by which Meena wins:

$500 - 375 = 125$ metres

Therefore, Meena wins by 125 metres.

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In a 500 metres race, the ratio of speeds of two participants Meena and Kamal is 4:5 respectively. If Meena has a start of 200 metres, find the distance by which Meena wins.

Solution

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