What is the ratio of the bikes’ time taken to cover the same distance if the speeds of 3 bikes are in the ratio 3 ∶ 5 ∶ 7?

Question

Question

This question was previously asked in

AAI ATC Junior Executive 21 Feb 2023 Shift 1 Official Paper

Answer 1

Given:

The speeds of three bikes are in the ratio

Formula used:

Speed = \(\frac{Distance}{Time}=\frac{d}{t}\)

Calculation:

Let the distance travelled by the bikes = \(d\)

And let the speeds of the three bikes be \(3x\), \(5x\) , and \(7x\).

Time taken by the 1^stbike to cover the distance \(t\) \(=\frac{d}{3x}\)

Time taken by the 2^nd bike to cover the distance \(t\) \(=\frac{d}{5x}\)

Time taken by the 3^rd bike to cover the distance \(t\) \(=\frac{d}{7x}\)

Ratio of time taken by the three bikes to cover the same distance

⇒ \(\frac{d}{3x}:\frac{d}{5x}:\frac{d}{7x}=\frac{1}{3}:\frac{1}{5}:\frac{1}{7}\)

Multiplying by LCM of 105

We get,

⇒ \(\frac{105}{3}:\frac{105}{5}:\frac{105}{7}=35:21:15\)

∴ The correct answer is the ratio of the bikes \(35:21:15\)\(\cdot\)