chetan2uI think I answered my own question. My brain is fried tonight for some reason. So I might as well double check.
In the question, Rahul is running those first X meters before Amit even starts.
“Head-start” in this sense means he started running for some time before Amit even left. It doesn’t mean that Rahul started at a line that was X meters ahead of where Amir started.
In other words, they both started running from the same starting line. Rahul just left earlier.
I don’t know why the word “head start” was causing my brain to close up.
chetan2u
prince00113
in a race, amit gave rahul a head start of 'x' m and took 20 sec to get ahead of rahul by 'x' m. Give that the ratio of sppeds of amit and rahul is 5:4 and rahul finished the race in 1 min. What fraction of race had amit completed when he overtook rahul?
a. 1/6
b. 5/24
c. 1/4
d. 7/24
e. 11/24
Let Rahul travel y in the time Amit goes up by x meter..
So Rahul travels =y and Amit travels = x+y+x
Now distance will be in same ratio as speed..
So \(\frac{y+2x}{y}=\frac{5}{4}....4y+8x=5y....y=8x\)
Rahul takes 1 min to complete but travels y or 8x in 20 secs..
So total distance=8x*60/20=24x..
Now Amit travels x+8x+x and covers 2x over Rahul..
So Amit will be equal to Rahul when he covers initial difference of x..
He will cover this in 10x/2=5x..
Fraction = 5x/24x=5/24
B
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