Question

In a 1000 m race, Ravi gives Vinod a start of 40 m and beats him by 19 seconds. If Ravi gives a start of 30 seconds, Vinod beats Ravi by 40 m. What is the ratio of the speed of Ravi to that of Vinod?

a. 3:2
b. 4:3
c. 5:4
d. 2:1

Answer 1

The ratio of the speed of Ravi to that of Vinod in the given race is 3:2. The correct answer is option a.

Step-by-step explanation:

In this question, we are given two scenarios involving Ravi and Vinod in a 1000m race. In the first scenario, Ravi gave Vinod a start of 40m and beat him by 19 seconds. In the second scenario, Ravi gave Vinod a start of 30 seconds and Vinod beat Ravi by 40m. We need to find the ratio of the speed of Ravi to that of Vinod.

Let's assume the speed of Ravi is x m/s and the speed of Vinod is y m/s.

In the first scenario, we can use the formula

Distance = Speed × Time.

Ravi covers a distance of 1000m in (1000-x) seconds and Vinod covers a distance of (1000-40)m in (1000-40-y) seconds.

From the given information, we can set up an equation:

1000-x = (1000-40-y) + 19

Simplifying this equation, we get:

x - y = 61 ----- equation (1)

In the second scenario, Ravi covers a distance of (1000-30)m in (1000-30-x) seconds and Vinod covers a distance of 1000m in (1000-y) seconds. From the given information, we can set up another equation:

(1000-30-x) = 1000 - y + 40

Simplifying this equation, we get:

x - y = 70 ----- equation (2)

We have a system of linear equations with equation (1) and equation (2).

Solving them simultaneously, we get x = 3.6 m/s and y = 2.4 m/s.

Therefore, the ratio of the speed of Ravi to that of Vinod is 3.6:2.4, which simplifies to 3:2.