Quantitative Aptitude -Time,Speed and Distance-Game or Race question-6!

PSA_LEVEL-UP_QNR40. Priyanka beats Jhumpu by 30 metres or 10 seconds. What is the speed of Priyanka and how much time was taken by Priyanka and Jhumpu respectively to complete the race of 1200 metres?

a) 3.07 m/s ; 6 min 30 s ; 6 min 40 s
b) 3.07 m/s ; 6 min 40 s ; 6 min 30 s
c) 4.07 m/s ; 6 min 10 s ; 6 min 30 s
d) 3.07 m/s ; 6 min 50 s ; 6 min 30 s
e) None of these

Ans:

Priyanka beats Jhumpu by 30 metres or 10 seconds. This means that-

(i) while Priyanka finishes 1200 metres in time ‘t’, Jhumpu could complete (1200-30) or 1170 metres in the same time. If speed of Priyanka and Jhumpu are Ss and Sk m/s respectively, then

Ss: Sk = 12001170 [Speed ratio would be same as the distance ratio when time is constant] —–(p)

(ii) Also, Jhumpu who is short by 30 metres takes 10 seconds to reach the finishing line. Thus, Jhumpu’s speed,
Sk = 3010 = 3m/s. —(q)

Using equations (p) and (q),

Ss/3 = 12001170

Ss=1200390 = 4013 m/s [= 3.07 m/s].

Time taken by Priyanka to complete the 1200 metres =1200(4013) = 1200*1340= 390 seconds = 6 mins 30 sec. Time taken by Jhumpu will be 10 seconds more i.e 6 mins 40 secs.

Alternatively, you could calculate the time in the below fashion as well:

Time taken by Priyanka to complete the 1200 metres = Time taken by Jhumpu to complete the 1170 metres= 11703 = 390 seconds. [= 6 mins 30 sec]

Time taken by Jhumpu to complete the 1200 metres = 12003= 400 seconds [= 6 mins 40 sec]. Option a.

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