Direction (Q. 1 - 5): Study the following information carefully and answer the given questions?

The following table shows the data related to speed of 5 different boats and the speed of current and also the ratio of downstream to that of upstream distance also given. Some values are missing here.

1) If boat Q travelled 110 km downstream in 5 hours, then find how much time boat Q will take to travel the upstream distance?

a) 8 hours

b) 6 hours

c) 5 hours

d) 7 hours

e) None of these

2) Boat P can cover certain distance downstream in 5 hours and it can cover the same distance upstream in 20 hours. Then find the ratio between the speed of boat in still water to that of stream of boat P (In km/hr), if the speed of downstream of boat P is twice the speed of downstream of boat T?

a) 5 : 3

b) 4 : 1

c) 7 : 4

d) 8 : 5

e) None of these

3) The ratio of speed of boat in still water to that of stream of boat S is 25 : 13 and the total time taken by boat S to cover the given upstream and downstream is 15 hours. Then find the distance covered by boat S in upstream?

a) 180 km

b) 120 km

c) 240 km

d) 90 km

e) None of these

4) If upstream distance covered by boat T is ‘x’ km while the downstream distance travelled by boat T is ‘x+ 300’ km and the time taken to travel downstream and upstream is equal, then find the value of x?

a) 250

b) 150

c) 200

d) 100

e) None of these

5) If the total upstream distance travelled by boat P and R in 8 hours is equal to 192 km while the speed of boat in still water of those boats is equal, then find time taken by boat R to travel downstream distance of 180 km. speed of stream in P is equal to speed of stream T

a) 6 hours

b) 7 hours

c) 5 hours

d) 8 hours

e) None of these

Answers:

1) Answer: C

Speed of downstream = 110 / 5 = 22 km/hr

Downstream distance = 110 km

Upstream distance = (110 / 11) * 4 = 40 km

Speed of boat in still water = 15 km/hr

According to the question,

Speed of boat in still water

= (Speed of downstream + Speed of upstream) / 2

(15 * 2) = (22 + Speed of upstream)

30 - 22 = Speed of upstream

Speed of upstream = 8 km/hr

Boat Q will take to cover 40 km upstream distance in,

= > (40 / 8) = 5 hours

2) Answer: A

Speed of downstream of boat T = 10 + 6 = 16 km/hr

Speed of downstream of boat P = 2 * 16 = 32 km/hr

Distance covered by boat P in downstream = 32 * 5 = 160 km

Speed of upstream of boat P = (160 / 20) = 8 km/hr

Speed of boat in still water of boat P = 32 + 8 = 40 km/hr

Speed of boat in stream of boat P = 32 - 8 = 24 km/hr

Required ratio = 40 : 24 = 5 : 3

3) Answer: B

The ratio of speed of boat in still water to that of stream of boat S = 25 : 13

Speed of boat in still water of boat S = 25 km/hr

Speed of boat in stream of boat S = (25 / 25) * 13 = 13 km/hr

Speed of downstream of boat S = 25 + 13 = 38 km/hr

Speed of upstream of boat S = 25 - 13 = 12 km/hr

According to the question,

(19x/38) + (12x/12) = 15

(x/2) + x = 15

(3x/2) = 15

x = 10

Total distance covered by boat S in upstream = 12x = 120 km

4) Answer: D

Speed of boat T in downstream= 10 + 6 = 16 km/hr

Speed of boat T inupstream= 10 - 6 = 4 km/hr

According to the question,

x / 4 = (x+ 300) / 16

4x= x+ 300

3x= 300

x = 100

5) Answer: A

Let the speed of boat P and R in still water be x km/hr,

Upstream speed of boat P = x-6

Upstream speed of boat R = x- 10

According to the question,

8 * (x-6) + 8 * (x - 10) = 192

8x – 48 + 8x – 80 = 192

16x- 128 = 192

16x= 320

x = 20 km/hr

So,

Downstream speed of boat R = 20 + 10 = 30 km/hr

Time taken to travel 180 km downstream = 180 / 30 = 6 hours