by how many metres will ajay beat anujay in a race of 400m if.....?

Question

in a race of 600m, ajay beats vijay by 60m and in a race of 500m vijay beats anujay by 25m.
please give the working steps also.

Answer 1

Let the speeds of Ajay, Vijay and Anujay be a, b and c.

Let the time taken by ajay to cover 600m be t.
Therefore, vijay covers (600-60)m = 540m in time t.
Speed of
ajay = 600/t
vijay = 540/t
a / b=10 / 9.................................Eq 1

Similarly,
Let the time taken by vijay to cover 500m be t.
Therefore, anujay covers (500-25)m = 475m in time t.
Speed of
vijay = 600/t
anujay = 540/t
b / c=20 / 19................................Eq 2

Multiply eq 1 by eq 2 -
a / c = 200 / 171

Therefore, the time in which Ajay covers 200m, Anujay will cover 171m
Or,
the time in which Ajay covers 400m, Anujay will cover 342m

Thus, jaya will beat anujay by 400-342m = 58m

I Hope that helped !!!

Answer 2

600/a = 540/v
500/v = 475/n
400/a = (400 - x)/n
a/n = 400/(400 - x)
a = 600v/540
v = 500n/475
a/n = 600*500/(540*475) = 400/(400 - x)
x = 400 - 400*540*475/(600*500)
x = 58 m