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

180 m

150 m

120 m

✅ Correct Option: 1

A starts the race 180 m ahead of the starting line, so A only needs to run 320 m while B runs the full 500 m.

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

A starts at 180 m and needs to cover $500 - 180 = 320$ m.

The ratio of speeds is A : B = 4 : 5.

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

Time = Distance ÷ Speed

Time taken by A to finish:

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

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

When A finishes at time $\dfrac{80}{x}$ , the distance covered by B is:

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

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

$\text{Distance} = 400$ m

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

Distance by which A wins:

$\text{Distance} = 500 - 400$

$\text{Distance} = 100$ m

Therefore, A wins by 100 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:

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:

Solution

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