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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?
Answer & Solution
Correct Answer:
Option
B
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.
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LoginVinay's speed 5
Bersha's speed 3
Atq 5t-3t= 1.5
t = .75
Time covered by vinay=.75*5*7
26.25km
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