Question

In racing over a given distance d at uniform speed, A can beat B by 30 meters, B can beat C by 20 meters and A can beat C by 48 meters Find 'd' in meters.
(1) 300
(2)350
(3)450
(4)400​

Answer 1

Answer:

450

Step-by-step explanation:

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Answer 2

Answer:

option a is correct

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Step-by-step explanation:

We are given a fixed distance ‘d’ meters.

Since A, B and C have uniform speed, let their speeds be a, b and c respectively.

We are given A can beat B by 30 meters

If A covers ‘d’ distance then B covers d−30

distance

Ratio of distance covered by A to distance covered by B is

⇒ab=dd−30

… (1)

We are given B can beat C by 20 meters

If B covers ‘d’ distance then C covers d−20

distance

Ratio of distance covered by B to distance covered by C is

⇒bc=dd−20

… (2)

We are given A can beat C by 48 meters

If A covers ‘d’ distance then C covers d−48

distance

Ratio of distance covered by A to distance covered by C is

⇒ac=dd−48

… (3)

We know ac=ab×bc

Substitute values in RHS form (1) and (2) and in LHS from equation (3)

⇒dd−48=dd−30×dd−20

Cancel same factor from numerator on both sides of the equation

⇒1d−48=1d−30×dd−20

Multiply terms in denominator of RHS

⇒1d−48=dd2−30d−20d+600

⇒1d−48=dd2−50d+600

Cross multiply the values from both sides of the equation

⇒d2−50d+600=d2−48d

Cancel same factor from both sides of the equation

⇒−50d+600=−48d

Shift -50d to RHS of the equation

⇒600=50d−48d

⇒600=2d

Cancel same factor from both sides of the equation

⇒300=d

∴

Distance is 300 meters