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Let the distance between A and B \(= b\)
Let the speed of X \(= a\) and therefore the speed of Y \(= 3a\)

Creating an equation from the following line 'X started from a point A towards point B. After 2 hours, Y started from B towards A. By the time X travelled one-fifth of the total distance, Y had also travelled the same.':

They both travelled \(\frac{1}{5}b\), however, as Y begins their journey, X will have already covered a distance of \(2a\) given that their speed is \(a\) and they will have travelled for \(2\) hours. This means that it takes X the same time to cover \(\frac{1}{5}b - 2a\) as it takes Y to travel \(\frac{1}{5}b\). As this is the case, we can make their respective time equations equal to one another.

\(\frac{\frac{1}{5}b - 2a}{a} = \frac{\frac{1}{5}b}{3a} \)

\(\frac{3}{5}ab - 6a^2 = \frac{1}{5}ab\)

\(\frac{2}{5}ab = 6a^2\)

\(\frac{2}{5}b = 6a\)

\(2b = 30a\)

\(b = 15a\)

Which means that it takes X: \(\frac{15a}{a} = 15\) hours to complete the trip, and it takes Y:  \(\frac{15a}{3a} = 5\)

\(15 - 5 = 10\)

ANSWER A

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How is this a <605 question­  :oops:
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Chose 2km/hr as for X and Y 6km/hr as speed, ie thrice. Then go ahead and multiply them by 3 and 1, as it leaves 2 hours late. You get they are 1/5th distance that is 6km, i.e 30 is total distance. Y will take 5 hours to reach and X will take 15, hence diff is just 10. I did this, took me 3 mins, anyone who can help me solve it faster?
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