Two persons A and B participated in a race of 1000 m. The ratio of the speeds of A and B is 3 : 5. B gives a head start of 100 m to A. Who will win the race and by how much distance?
Correct Answer : d ) B will win by 300 mExplanation :
We know, Distance = speed × time
As, the race will be finished for both A and B at the same time
We know, Distance = Speed × Time
So, for same time, ratio of the distances covered by A and B during the race will be equal to the ratio of the speed of A and B
Ratio of speed of A and B = 3 : 5
⇒ Ratio of distances covered by A and B = 3 : 5
Let us assume distance covered by A during the race be 3x and that by B be 5x
Case 1: If A wins the race, distance covered by him will be = 1000 – 100 (head start) = 900 m
Thus, 3x = 900
x = 300 m
Distance covered by B = 5x = 5*300 = 1500 m (NOT POSSIBLE)
Case 2: If B wins the race, distance covered by him will be = 1000 m
Thus, 5x = 1000
x = 200 m
Distance covered by A = 3x = 3*200 = 600 m
Now, B beat A by = 1000 – (600 + 100) ……… (A has been given a head start of 100 m)
Thus, B beats A by 300 m
Hence, (d) is the correct answer.
Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, UPSC NDA, UP SI etc.