BANK & INSURANCE (BOAT AND STREAM) PART 2

ATQ,

(x + y) = (196/9.8) = 20 …… (I)

And, (x - y) = (55/5.5) = 10 …… (II)

By adding equation (I) and equation (II), we get,

2x = 30

x = 15

From equation (I), we get

y = 5

So, speed of boat in still water = 15 km/hr

And, speed of stream = 5 km/hr

Now,

Increased speed of boat in still water = (15 + 6) = 21 km/hr

Decreased speed of stream = (5 - 2) = 3 km/hr

Required time = {(216/(21 + 3)) + (144/(21 - 3))}

= (9 + 8) = 17 hours

Then, downstream speed of the boat = 9x × (11/9)

= 11x km/h

According to the question,

(135/9x) - (132/11x) = (45/60) = 0.75

(15/x) - (12/x) = 0.75

x = (3/0.75)

x = 4

So, speed of the boat in still water = {(upstream speed + downstream speed)/2}

= (9x + 11x) ÷ 2 = 10x

= 40 km/h

= 35 km/h

Let the speed of the stream = ‘y’ km/h

Then, we have, (35 - y) = (35 + y) × 0.75

Or, 35 - y = 26.25 + 0.75y

Or, 8.75 = 1.75y

So, y = 8.75 ÷ 1.75 = 5

So, upstream and downstream speed of the boat is 30 km/h and 40 km/h, respectively.

So, total distance travelled by the boat = 40 × 1 + 30 × (110/60)

= 40 + 55 = 95 km

So, upstream speed of the boat = 116.2 ÷ 4.15

= 28 km/h

Distance travelled by the boat travelling upstream for 2.5 hours = 28 × 2.5 = 70 km

So, distance travelled by the boat travelling downstream for 3 hours = 178 - 70 = 108 km

So, downstream speed of the boat = 108 ÷ 3

= 36 km/h

Therefore, speed of the boat in still water = (36 + 28) ÷ 2 = 32 km/h

The speed of boat in still water = 8 km/hr

Speed of boat against the stream = (8 - y) km/hr

Speed of boat against the stream = 3 × (60/36) = 5 km/hr

So, (8 - y) = 5

y = 8 - 5

y = 3

Speed of boat with the stream = (8 + y) = (8 + 3) = 11 km/hr

The time taken by the boat to cover a distance of 49.5 kilometres with the stream = (49.5/11) = 4.5 hours

So, speed of boat in still water = 4x + 4x × 1.25 = ‘9x’ km/h

So, downstream speed of the boat = (9x + 4x) = ‘13x’ km/hr

So, upstream speed of the boat = (9x - 4x) = ‘5x’ km/hr

According to question:

(195/13x) + (125/5x) = 40

(15/x) + (25/x) = 40

40x = 40

x = 1

So, speed of boat in still water = (9 × 1) = 9 km/hr

Required time = (216/9) = 24 hours

So, speed of the stream = 10x × 0.3 = ‘3x’ km/h

ATQ,

10x + 3x = 195 ÷ 6

Or, 13x = 32.5

So, x = 2.5

So, speed of the boat in still water = 2.5 × 10 = 25 km/h

Upstream speed of the boat = 10x - 3x = 7x = 17.5 km/hr

So, required time = (195/25) + (73.5/17.5)

= 7.8 + 4.2 = 12 hours

= 48 km/h

Speed of the stream = 48 × (3/8) = 18 km/h

So, speed of the boat in still water = 48 - 18 = 30 km/h

So, required time taken = (360/30) = 12 hours

Let the speed of the stream = ‘y’ km/h

Then, upstream and downstream speeds of boat ‘P’ is (28 - y) km/h and (28 + y) km/h, respectively

According to the question,

(28 - y) = (28 + y) × 0.75 = (21 + 0.75y)

21 + 1.75y = 28

So, y = 7 ÷ 1.75 = 4

So, downstream speed of boat ‘P’ = 28 + 4 = 32 km/h

And so, upstream speed of boat ‘Q’ = 32 × (15/16) = 30 km/h

So, still water speed of boat ‘Q’ = 30 + 4 = 34 km/h

Time taken to travel 68 km downstream = (68/17) hrs. = 4 hrs.