# Important Formulas

# Problems on Boats Stream

Q1. A man can row upstream at 10 km/hr and downstream at
16 km/hr. The speed of the stream is ?

(a) 2 Km/hr

(b) 3 Km/hr

(c) 8 Km/hr

(d) 15 Km/hr

**Answer:** (b) 3 Km/hr

Speed of Stream = 1/2 (16-10) km/hr = 3 Km/hr

Q2. A boat can travel 15 km/ hr in still water. If the
speed of the the stream is 3 km/hr, then what will be the
time taken by the boat to travel 72 km in downstream
direction ?

(a) 3 hrs

(b) 4 hrs

(c) 6 hrs

(d) 12 hrs

**Answer:** (b) 4 hrs

Relative Speed in Downstream direction = (15+3) km/hr = 18 Km/hr

So time taken to travel 72 km = (72/18) km/hr = 4 hrs

Q3. A boat can travel 10 km/ hr in still water. If the
speed of the the stream is 6 km/hr, then what will be the
time taken by the boat to travel 40 km in upstream
direction ?

(a) 8 hrs

(b) 9 hrs

(c) 10 hrs

(d) 12 hrs

**Answer:** (c) 10 hrs

Relative Speed in Upstream direction = (10 - 6) km/hr = 4 Km/hr

So time taken to travel 40 km = (40/4) km/hr = 10 hrs

Q4. The speed of a current is 5 km/hr and a man's speed
against the current is 18 km/hr. So the man's speed with the
current is ?

(a) 28 km/hr

(b) 23 km/hr

(c) 20 km/hr

(d) 16 km/hr

**Answer:** (a) 28 km/hr

Speed in still water = (5 + 18) km/hr =23 km/hr

So the man's speed with the current is = (23 + 5) km/hr = 28 km/hr

Q5. A boat can covers a distance of 12 km in 4 hours in
downstream direction, while the same distance covers in 6
hours in upstream direction. What is the speed of the boat in
still water ?

(a) 2 km/hr

(b) 2.5 km/hr

(c) 3.5 km/hr

(d) 5 km/hr

**Answer:** (b) 2.5 km/hr

Rate in downstream direction = (12/4) km/hr = 3 km/hr

Rate in upstream direction = (12/6) km/hr = 2 km/hr

so speed in still water = 1/2 (3 + 2) = 2.5 Km/hr

Q6. A boat can travel with a speed of 9 km/hr in still
water. If the speed of the stream is 3 km/hr, then what time
will be taken by boat to travel 60 km in downstream
direction ?

(a) 2 hr

(b) 3 hr

(c) 5 hr

(d) 8 hr

**Answer:** (c) 5 hr

Speed in downstream direction = 9 + 3 =12 km/hr

So Time taken to travel 60 km in downstream direction

= (60/12) = 5 hr

Q7. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is

(a) 2 mph

(b) 3 mph

(c) 3.5 mph

(d) 5 mph

**Answer:** (a) 2 mph

Let the speed of the stream be x mph

Then Speed downstream = (10+x) mph

Speed upstream = (10-x) mph

(36/(10-x)-36/(10+x)) = 90/60

72xX60 = 90(100 - x^{2})

x^{2} + 48x + 100 = 0

(x+50) + (x-2) = 0

x = 2

Q8. The speed of a boat in still water is 10 km/hr. If it can travel 26 km downstream and 14 km upstream in the same time, the speed of the stream is

(a) 2 km/hr

(b) 3 km/hr

(c) 5 km/hr

(d) 7 km/hr

**Answer:** (b) 3 km/hr

Let the speed of the stream be x km/hr

Then Speed downstream = (10+x) km/hr

Speed upstream = (10-x) km/hr

(26/(10+x)) = 14/(10-x)

260 - 26x = 140 + 14x

40x = 120

x = 3 km/hr

Q9. A boat is rowed downstream at 16.5 km/hr and upstream at 9.5 km/hr. The speed of the stream is

(a) 3.5 km/hr

(b) 4 km/hr

(c) 5.3 km/hr

(d) 7.8 km/hr

**Answer:** (a) 3.5 km/hr

Speed of the stream = 1/2 (16.5 - 9.5) km/hr

= 1/2 X 7 km/hr

= 3.5 km/hr

Q10. A boatman goes 3km against the current of stream in 1hr and goes 2km along the current in 20 minutes. How long will he take to go 6km in stationary water

(a) 1.5 hr

(b) 1(1/3) hr

(c) 2.5 hr

(d) 2(1/3) hr

**Answer:** (b) 1(1/3) hr

Upstream speed = 3 km/hr

Downstream speed = 6 km/hr

Speed in stationary water = 1/2(3+6) km/hr

= 4.5 km/hr

Time taken to cover 6km in stationary water = 6/4.5 hr = 60/45 = 4/3 = 1(1/3)hr