Let speed of boat Upstream be - $U$
Let speed of boat Downstream be - $D$
Let speed of boat in still water be - $B$
Let speed of stream be - $W$
$U = B - W$
$D = B + W$
Given on Saturday:
$B_{sat} = 27 \text{ kmph}$
On Wednesday:
$B_{wed} = B_{sat} + 66\frac{2}{3}\% \times B_{sat}$
$B_{wed} = 27 + \frac{200}{3} \times \frac{27}{100} = 45 \text{ kmph}$
Let time taken to travel downstream on Saturday be - $t$
Time taken to travel upstream on Wednesday $= \frac{16}{13}t$
On Wednesday:
$W_{wed} = 6 \text{ kmph}$
$U_{wed} = B_{wed} - W_{wed} = 45 - 6 = 39 \text{ kmph}$
Distance travelled upstream on Wednesday $= 12\% \text{ of } 4800 = 576 \text{ km}$
Time taken upstream on Wednesday $= \frac{576}{39} = \frac{192}{13} \text{ hours}$
$\frac{16}{13}t = \frac{192}{13}$
$t = 12 \text{ hours}$
Time taken downstream on Saturday $= 12 \text{ hours}$
Distance covered downstream on Saturday $= 432 \text{ km}$
Speed downstream on Saturday $= \frac{432}{12} = 36 \text{ kmph}$
$D_{sat} = B_{sat} + W_{sat}$
$36 = 27 + W_{sat}$
$W_{sat} = 9 \text{ kmph}$
Therefore, speed of stream on Saturday is $9 \text{ kmph}$
