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?
A. 25.25 km
B. 26.25 km
C. 13.2 km
D. 14.5 km
Answer: Option B
Solution (By Examveda Team)
Since, the speeds of Vinay and Versha are in the ratio 5 : 3 i.e. when Vinay covers 5 rounds, then Versa covers 3 rounds, but first time Vinay and Versha meet when Vinay completes $$\left\{ {2\frac{1}{2} = 2.5} \right\}$$ round and Versha completes $$\frac{1}{2}$$ round. For Vinay to pass Versha seventh time, Vinay would have completed, = 7 × 2.5 rounds Since, each round is 1.5 km, the distance covered by Vinay is, = 7 × 2.5 × 1.5 = 26.25 km.This Question Belongs to Arithmetic Ability >> Speed Time And Distance
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