Vinay and Versha run a race with their speed in the ratio of 5 : 3. They prefer to run on a circular track of circumference 1.5 km. What is the distance covered by Vinay when he passes Versha for the seventh time?

Let theirs meeting time t sec
Vinay's speed 5
Bersha's speed 3
Atq 5t-3t= 1.5
t = .75
Time covered by vinay=.75*5*7
26.25km

Assume Vinay passes Versha for the seventh time in
t
hours

Let the distance travelled by Versha during
t
hours
=
x
km

Distance travelled by Vinay during
t
hours
=
(
x
+
10.5
)
km
(we added 10.5 km because in t hours, Vinay travelled
7
×
1.5
=
10.5
km more than Versha)

i.e., Distance travelled by Vinay in
t
hr : Distance travelled by Versha in
t
hr
=
(
x
+
10.5
)
:
x


Speed of Vinay : Speed of Versha
=
5
:
3


Distance travelled is directly proportional to the speed. Therefore,
(
x
+
10.5
)
:
x
=
5
:
3
3
x
+
31.5
=
5
x
2
x
=
31.5
x
=
15.75


Distance covered by Vinay when he passes Versha for the seventh time
=
(
x
+
10.5
)
=
(
15.75
+
10.5
)
=
26.25
km

how did u get after 2.5 around they will meet?

Please explain the step=how you had taken 2(1/2)=2.5 round for vinay and o.5 round for versha