Ratio And Proportion

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Before water is added, the mixture's entire volume is : = .

The ratio of milk to water after adding three liters is , therefore .

To determine the values of , , and , we can solve these equations.

Equations (2) and (3) give us:

Substitute from equation (2) into the above equation, we get:

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Replacing into equation (1), we get:

cross multiplying, we get:

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Therefore, x is 3.

• Distance of the race = 600 m
• Speed ratio of A to B = 4:5
• Head start for A = 200 m

• Since A gets a head start of 200 m, A only needs to cover (600 - 200) = 400 m to finish the race.

• Let's assume the speed of A = 4x and speed of B = 5x.
• Time taken by A to cover 400 m = Distance/Speed = 400/(4x) = 100/x
• Time taken by B to cover 600 m = Distance/Speed = 600/(5x) = 120/x

• Since 100/x < 120/x, A finishes the race before B.
• In 100/x time, B would have covered 5x * (100/x) = 500 m.
• Therefore, when A finishes, B is at 500 m.
• The distance by which A wins = Total distance for B - Distance covered by B = 600 - 500 = 100 m.