Question

In a race of 1000 meters, A can beat B by 100 m. In a race of 800 meters, B can beat C by 100 meters. By how many meters will A beat C in a race of 600 meters?

Answer 1

Hint: In order to solve this question, we should know the concept of unitary method, we will first calculate the distance travelled by C when B runs for 1 meter and then we will find the distance travelled by C when A runs for a distance of 1 meter and then we will multiply that by 600, to get the answer.

Complete step-by-step answer:

In this question, we have been asked to find by how many meters A will beat C in a race of 600 m, when it is given that A beats B by 100 m in a race of 1000 m and B beats C by 100 m in a race of 800 m.

Now, we have been given that A beats B by 100 m in a race of 1000 m. So, we can say that if A runs 1000 m then, B runs 900 m. We have also been given that, B beats C by 100 m in a race of 800 m. So, we can say that if B runs 800 m, then C runs 700 m.

Therefore, we can say that if B runs 1 m then, C runs $\dfrac{700}{800}m$, and if B runs 900 m, then C runs $\dfrac{700\times 900}{800}m$. And we know that when B runs 900 m, then A runs 1000 m. So, we can say that if A runs 1000 m, then C runs $\dfrac{700\times 900}{800}m$.

Now, we can say that if A runs 1 m, then C runs $\dfrac{700\times 900}{800\times 1000}m$. And further we can say that, if A runs 600 m, then C will run $\dfrac{700\times 900\times 600}{800\times 1000}m$. Hence, we get, if A runs 600 m, then C runs 472.5 m.

Therefore, we can say, in a race of 600 m, A can beat C by (600-472.5) m = 127.5 m.

Note: At the time of reading this question, we might get confused because we have relation for A and B and also for B and C, but we have been asked to find the relation for A and C. So, we will simply find the relation of B and C for that much meter of distance as much as it can when A runs 1000 m and then get the answer.