A man can row against the current three-fourth of a kilometre in 15 min and returns same distance in 10 min, then ratio of his speed to that of current is?

Let the speed of man and current be U and V km/h, respectively.
Speed upstream = (U - V) km/h
Speed down stream = (U + V) km/h
According to the question,
(3 x 60)/(4 x 15) = U - V
⇒ U - V = 3 ......(i)
and (3/4) x (60/10) = U + V
⇒ U + V = 9/2 ...(ii)
On adding Eqs. (i) and (ii), we get
2U = 3 + 9/2
⇒ U = 15/4
On putting the value of U in Eq. (ii), we get
15/4 + V = 9/2
V = 9/2 - 15/4 = 18 - 15/4
⇒ V = 3/4
Hence, speed of man U = 15/4 and
Speed of current V = 3/4
Hence, required ratio = 15/4 : 3/4 = 5 : 1