Arithmetic

Time, Speed & Distance

Medium

applied

In a 500 m race, the ratio of speeds of two participants, A and B, is 4:5 respectively. If A has a start of 180 m, then the distance by which A wins is

100 m

120 m

110 m

80 m

✅ Correct Option: 1

The total race distance is 500 m. A gets a head start of 180 m, and the speed ratio of A:B is 4:5.

A starts at 180 m and needs to reach 500 m.

Distance A needs to run $= 500 - 180 = 320$ m

B starts at 0 m and needs to reach 500 m.

Distance B needs to run $= 500$ m

Given speed ratio A:B $= 4:5$

Let A's speed $= 4x$ and B's speed $= 5x$

Time taken by A to finish:

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

$\text{Time for A} = \dfrac{320}{4x}$

$\text{Time for A} = \dfrac{80}{x}$

Time taken by B to finish:

$\text{Time for B} = \dfrac{500}{5x}$

$\text{Time for B} = \dfrac{100}{x}$

Since $\dfrac{80}{x} < \dfrac{100}{x}$ , A finishes first.

When A crosses the finish line at time $= \dfrac{80}{x}$ , the distance covered by B is:

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

$\text{Distance by B} = 5x \times \dfrac{80}{x}$

$\text{Distance by B} = 400$ m

When A finishes at 500 m, B is at 400 m.

Distance by which A wins $= 500 - 400 = 100$ m

Therefore, A wins by 100 m.

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In a 500 m race, the ratio of speeds of two participants, A and B, is 4:5 respectively. If A has a start of 180 m, then the distance by which A wins is

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