A boat goes 24 km upstream and 28 km downstream in 6 hours. It goes 30km upstream and 21 km downstream in 6 hours and 30 minutes. The speed of the boat in still water is :

Options

A. 8 किमी/घंटा
B. 9 किमी/घंटा
C. 12 किमी/घंटा
D. 10 किमी/घंटा

Answer

D

Explanation

`(24)/(x-y) + (28)/(x+y) = 6`
`(30)/(x-y) + (21)/(x+y) = (13)/(2)`
माना x+ y = U
तथा x-y = V
`(24)/(V) + (28)/(U) = 6 ………….. (i)`
`(30)/(V) + (21)/(U) = (13)/(2) ……… (ii)`
समी. (i) `xx` 5- समी. (ii) `xx` 4

`implies U = 14`
समी. (i) में U का मान रखने पर
`(24)/(V) = 6-2`
`(24)/(V) = 4`
`implies V = 6`
`x+y = 14 ............(iii) " "(because U = x+ y)`
`x-y = 6 ............. (iv) " "(because V = x-y)`
समी. (iii) + समी. (iv)
2x= 20
`therefore ` x= 10 km/h
अतः नाव की शांत जल में गति = 10 km/h