Arithmetic

Time, Speed & Distance

Medium

applied

In a 700 m race, the ratio of speeds of two participants A and B is 5:6. If A has a start of 150 m, then the distance by which A wins the race is:

80 m

40 m

75 m

100 m

✅ Correct Option: 2

In a 700 m race, A has a start of 150 m and B starts at 0 m. The speed ratio of A to B is 5:6.

A's actual running distance = 700 - 150 = 550 m

B's actual running distance = 700 - 0 = 700 m

Given speed ratio A:B = 5:6

A's speed = 5x

B's speed = 6x

Time taken by A to finish the race:

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

Time = $\dfrac{550}{5x}$

Time = $\dfrac{110}{x}$

Distance covered by B in the same time:

Distance = Speed × Time

Distance = $6x \times \dfrac{110}{x}$

Distance = $660$ m

When A reaches the finish line at 700 m, B is at 660 m.

Distance by which A wins = 700 - 660 = 40 m

Therefore, A wins the race by 40 m.

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In a 700 m race, the ratio of speeds of two participants A and B is 5:6. If A has a start of 150 m, then the distance by which A wins the race is:

Solution

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