PSA_LEVEL-UP_QNR39. In a race of 600 metres, Ajay beats Vijay by 60 metres and in a race of 500 metres Vijay beats Anjay by 25 metres. By how many metres will Ajay beat Anjay in a 400 metre race?
a) 48 m
b) 52 m
c) 56 m
d) 58 m
Let speeds of Ajay, Vijay and Anjay be Sa, Sv and San units.
In a race of 600 metres, Ajay beats Vijay by 60 metres. This means that while Ajay covers 600 metres in time ‘t’, Vijay has covered only (600-60) or 540 metres in the same time.
If time is constant, speed ratio is same as the distance ratio.
Sa: Sv = 600:540 = 10:9 —(p)
Similarly, in a race of 500 metres, Vijay beats Anjay by 25 metres. This means that while Vijay covers 500 metres in time ‘t1’, Anjay has covered only (500-25) or 475 metres in the same time.
Sv: San = 500:475 = 20:19 —(q)
Since, we have to find out the result when Ajay and Anjay compete in a race, let us find out the ratio of speed of Ajay and Anjay.
Multiplying equations (p) and (q),
(Sa/Sv) * (Sv/San) = (10/9) * (20/19)
=>Sa/San = 200/171
=>Sa/San = (2*200)/(2*171)
=>Sa/San = 400/342 [Expressing the numerator in terms of 400 which is equal to the race length].
The above expression shows that while Ajay covers 400 metres in some time, Anjay has been able to finish only 342 metres in the same time. Ajay beats Anjay by (400-342) or 58 metres. Option d.