A boat takes total 03 hrs. to cover a distance of 12 km in upstream and comes back 18 km in downstream. While the boat takes 6.5 hrs. to cover a distance of 36 km in upstream and comes back 24 km in downstream. Find speed of the current.

02 km/hr

\(\frac{12}{x - y}\) + \(\frac{18}{x + y}\) = 3   ---(i)

\(\frac{36}{x - y}\) + \(\frac{24}{x + y}\) = 6.5   ---(ii)

(i) x 3 - (ii) x 1 

\(\frac{30}{x + y}\) = 2.5

x + y = 12,

Put in equation (ii)

\(\frac{36}{x - y}\) + \(\frac{24}{12}\) = 6.5

\(\frac{36}{x - y}\) + 2 = 6.5

\(\frac{36}{x - y}\) = 4.5

\(\frac{36}{4.5}\) = x - y

x - y = 8

Now add & subtract x + y & x - y

x = 10, y = 2