Up and Down Both MCQ Quiz - Objective Question with Answer for Up and Down Both - Download Free PDF

Given:

Downstream distance = 64 km

Time taken for downstream = 4 hours

Upstream distance = 48 km

Time taken for upstream = 6 hours

Formula used:

Speed = Distance ÷ Time

Speed downstream = (Speed of boat + Speed of current)

Speed upstream = (Speed of boat - Speed of current)

Calculations:

Speed downstream = 64 ÷ 4 = 16 km/hr

Speed upstream = 48 ÷ 6 = 8 km/hr

Let the speed of the boat in still water be 'b' km/hr and the speed of the current be 'c' km/hr.

Speed downstream = b + c = 16

Speed upstream = b - c = 8

Now, solving the equations:

b + c = 16

b - c = 8

Add the two equations:

(b + c) + (b - c) = 16 + 8

2b = 24

b = 12 km/hr

The speed of the boat in still water is 12 km/hr.

Now, the distance covered by the boat in 5 hours in still water is:

Distance = Speed × Time

Distance = 12 × 5 = 60 km

∴ The distance covered by the boat in 5 hours in still water is 60 km.

Calculation

Let downstream speed is 8x.

So, upstream speed is 8x × 5/  8 = 5x

So, [8x - 5x]/2 = 3

So, x = 2

So, upstream speed is 10 and downstream speed is 16

Let, Distance is D.

So, D/16 + D /10 = 7 (48/60) = 39/5

Or, 13D/80 = 39/5

Or, D = 48 km

Total distance is 48 + 48 = 96 

Given:

Distance from A to B = 2 km

Total distance (round trip) = 4 km

Speed of stream = 3 km/hr

Total time taken = 30 min = 0.5 hr

Let speed of motor boat in still water = x km/hr

Formula used:

Downstream speed = x + 3

Upstream speed = x - 3

Time = Distance ÷ Speed

Total time = Time down + Time up

Calculation:

\(\frac{2}{x+3} + \frac{2}{x-3} = 0.5\)

⇒ 2(x - 3) + 2(x + 3) = 0.5(x2 - 9)

⇒ 2x - 6 + 2x + 6 = 0.5(x2 - 9)

⇒ 4x = 0.5x2 - 4.5

⇒ x2 - 8x - 9 = 0

Solve the quadratic:

⇒ (x - 9) (x + 1) = 0

⇒ x = 9 or x = -1 

∴ Speed of motor boat in still water is 9 km/hr

Calculation

Let downstream speed is 8x.

So, upstream speed is 8x × 5/  8 = 5x

So, [8x - 5x]/2 = 3

So, x = 2

So, upstream speed is 10 and downstream speed is 16

Let, Distance is D.

So, D/16 + D /10 = 7 (48/60) = 39/5

Or, 13D/80 = 39/5

Or, D = 48 km

Total distance is 48 + 48 = 96 

Given:

Speed of the stream = 8 km/h

Downstream distance = 19 km

Upstream distance = 9 km

Total time = 4 hours

Formula used:

Time = Distance / Speed

Calculation:

Speed of the boat in still water = x km/h

Speed downstream = (x + 8) km/h

Speed upstream = (x - 8) km/h

Time downstream = 19 / (x + 8)

Time upstream = 9 / (x - 8)

⇒ Total time = Time downstream + Time upstream

⇒ 4 = 19 / (x + 8) + 9 / (x - 8)

⇒ Multiply both sides by (x + 8)(x - 8) to eliminate the denominators:

⇒ 4(x + 8)(x - 8) = 19(x - 8) + 9(x + 8)

⇒ 4(x² - 64) = 19x - 152 + 9x + 72

⇒ 4x² - 256 = 28x - 80

⇒ 4x² - 28x - 176 = 0

⇒ Divide the equation by 4:

⇒ x² - 7x - 44 = 0

Solving this quadratic equation:

Using the quadratic formula: x = [-(-7) ± √((-7)² - 4 × 1 × (-44))] / 2 × 1

⇒ x = [7 ± √(49 + 176)] / 2 = [7 ± √225] / 2 = [7 ± 15] / 2

⇒ x = (7 + 15) / 2 = 22 / 2 = 11

∴ The speed of the boat in still water = 11 km/h

Concept used:

If upstream speed = U and downstream speed = D, then speed of boat = (U + D)/2

Calculation:

According to the question,

20/U + 44/D = 8  … (i)

15/U + 22/D = 5  … (ii)

Multiply by 2 the equation (ii) then subtract from 1 we get

20/U + 44/D = 8

30/U + 44/D = 10

- 10/U = - 2

⇒ U = 5 km/hr

Putting the value in equation (i), we get D = 11

So, the speed of boat = (U + D)/2 = (5 + 11)/2 = 8 km/hr

∴ The correct answer is 8 km/hr

Given:

A man rows a boat a certain distance downstream in 9 hours, while it takes 18 hours to row the same distance upstream. ​

Concept used:

1. Distance = Speed × Time

2. While rowing upstream, the upstream speed is the difference between the speed of the boat in still water and the speed of the flow.

3. While rowing downstream, the downstream speed is the addition of the speed of the boat in still water and the speed of the flow.

4. Componendo-Dividendo Method

Calculation:

Let the distance, speed of the boat in still water, and speed of the river be D, S, and R respectively.

​According to the concept,

D/(S - R) = 18      ....(1)

D/(S + R) = 9      ....(2)

(1) ÷ (2),

(S + R)/(S - R) = 2

⇒ \(\frac {S + R + S - R}{S + R - S + R} = \frac {2 + 1} {2 - 1}\) (Componendo-Dividendo Method)

⇒ \(\frac {S}{R} = 3\)

⇒ S = 3R

Putting S = 3R in (1), D = 36R

Now, time taken to row three-fifth of the same distance in still water = \(36R \times \frac {3}{5} \div 3R\) = 7.2 hours

∴ It will take 7.2 hours to row three-fifth of the same distance in still water.

Shortcut Trick

Let's assume the total distance be 180 km

So, down-stream speed will be 180/9 = 20 km/hr

So, up-stream speed will be 180/18 = 10 km/hr

Now, speed of the boat will be (20 + 10)/2 = 15 km/hr

So,the boat can row (3/5^th of 180km) 108 km in 108/15 = 7.2 hr

Given: 

A swimmer swims from point P against the current for 6 min and then swims back along the current for next 6 min and reaches at a point Q.

The distance between P and Q is 120 m.

Concept used:

1. 6 min = 360 seconds

2. While rowing upstream, the upstream speed is the difference between the speed of the boat in still water and the speed of the flow.

3. While rowing downstream, the downstream speed is the addition of the speed of the boat in still water and the speed of the flow.

4. 1 m/s = 18/5 km/h

5. Distance = Time × Speed

Calculation:

Let's suppose the swimmer started from P and swam 360 seconds to R against the current, then return to Q swimming for 360 seconds.

Let the speed of the swimmer in still water and the current be U and V m/s respectively.

​According to the question,

PR = 360(U - V)      ....(1)

QR = 360(U + V)      ....(2)

So, PQ = QR - PR

⇒ 120 = 360(U + V - U + V) (From 1 and 2)

⇒ V = 1/6

So, the speed of the current = 1/6 m/s

Now, the speed of the current = 1/6 × 18/5 = 0.6 km/h

∴ The speed of the current is 0.6 km/h.

Given:

The speed of the motorboat in still water = 20 km/h

Concept used:

If the speed of a boat in still water is x km/h and the speed of the stream is y km/h, then

Downstream speed = (x + y) km/h

Upstream speed = (x - y) km/h

Time = Distance/Speed

Calculation:

According to the question, the motorboat takes 30 minutes more to go 24 km upstream than to cover the same distance downstream.

Let, the speed of the water = x km/h

So, 24/(20 - x) = 24/(20 + x) + (1/2)  [∵ 30 minutes = 1/2 hour]

⇒ 24/(20 - x) - 24/(20 + x) = (1/2)

⇒ \(\frac{24(20+x)-24(20-x)}{400-x^2}=\frac{1}{2}\)

⇒ \(\frac{24(20+x-20+x)}{400-x^2}=\frac{1}{2}\)

⇒ \(\frac{24×2x}{400-x^2}=\frac{1}{2}\)

⇒ 400 - x² = 96x

⇒ x² + 96x - 400 = 0

⇒ x2 + 100x - 4x - 400 = 0

⇒ x (x + 100) - 4 (x + 100) = 0

⇒ (x + 100) (x - 4) = 0

⇒ x + 100 = 0 ⇒ x = -100 ["-" is neglacted]

⇒ x - 4 = 0 ⇒ x = 4

∴ The speed of the water = 4 km/h

The speed of the motorboat in still water increased 2 km/h = 20 + 2 = 22 km/h

The time for 39 km downstream and 30 km upstream = 39/(22 + 4) + 30/(22 - 4) hours

= (39/26) + (30/18) hours

= 3/2 + 5/3 hours

= 19/6 hours

= (19/6) × 60 minutes

= 190 minutes

= 3 hours 10 minutes

∴ The motorboat will take 3 hours 10 minutes to go 39 km downstream and 30 km upstream

Shortcut TrickValue putting method, 

According to the question, 

30 min = 1/2 hr

x = 20 (Speed in still water)

⇒ 24/(20 - y) - 24/(20 + y) = 1/2

Here the R.H.S is 1/2, so the value of 20 - y must be more than 12

Hence take y = 4 (so that right bracket will become 1 as 20 + 4 = 24) and (left bracket will be more than half)

⇒ 24/(20 - 4) - 24(20 + 4) = 3/2 - 1 = 1/2

Hence the value of Y = 4

Now according to the question, 

⇒ 39/(22 + 4) + 30/(22 - 4) = 39/26 + 30/18

⇒ 19/6 = 3(1/6) = 3 hours and 10 min

∴ The motorboat will take 3 hours 10 minutes to go 39 km downstream and 30 km upstream

Given:

A boat can go 60 km downstream and 40 km upstream in 12 hours 30 minutes.

It can go 84 km downstream and 63 km upstream in 18 hours 54 minutes.

Concept used:

Upstream speed = Boat speed - speed of the current 

Downstream speed = Boat speed + speed of the current

Distance = speed × time

Calculation:

Downstream speed = x km/h

The upstream speed=  y km/h

As per the question,

60 /x + 40/y = 25/2 ...... (1)

Again, 84/x + 63/y = 189/10 ....... (2)

By solving 1 and 2 we get,

x = 40 / 3 and y = 5

So Still water boat's speed is

⇒ (13..33 + 5) / 2 = 9km/hr

∴ The correct option is 3

Alternate Method 

Let the speed of the boat = u

and

speed of current/river = v

So,

upstream speed (US) = u - v

downstream speed (DS) = u + v

according to the question,

60/DS  +  40/US  = 12.5

⇒ 3/DS + 2/US = 0.625 ....(1)

and

84/(u + v)  + 63/(u - v) = 18.9

⇒ 4/DS + 3/US = 0.9 ....(2)

let 

a = 1/DS   and  b = 1/US

then eq(1) and eq(2) will be

⇒ 3a + 2b  = 0.625 ....(3)

⇒ 4a  + 3b = 0.9....(4)

So, multiply eq(3) with 3 and eq(4) with 2:-

⇒ 9a + 6b = 1.875  ...(5)

⇒ 8a + 6b = 1.8 ....(6)

now,  eq(5) - eq(6)

a = 0.075

then DS = 40/3

and from eq(6)

6b = 1.2

⇒ b = 0.2

⇒ US = 5

Boat speed = (DS + US)/2 = 55/6

Hence; u ≈ 9 km/hr

Given:

Total distance = 24km

Time taken = 7/4 hours

Concept used:

Speed = D/t

D= Distance

t = time

Calculation:

Let the speed of man and current be v and s respectively. 

According to the question,

\({8\over v \;+\;s} = {6\over v \;-\;s}\)

⇒ 8v - 8s = 6v + 6s

⇒ 2v = 14s

⇒ v : s = 7 : 1

Let speed of man = 7x

Speed of current = x

So,

24/8x + 24/6x = 7/4

⇒ 3/x + 4/x = 7/4

⇒ 7/x = 7/4

⇒ x = 4

⇒ speed of the current = 4 km/h

∴ The speed of the current is 4 km/h

Given : 

Speed of boat a down the stream is 125% of the speed in still water.

Boat takes 30 minutes to cover 20 km in still water.

Concept Used :

Downstream Speed = D/v + u

Upstream Speed = D/v - u

v = Speed of boat, u = Speed of stream

Calculation : 

⇒ v+ u/v = 125/100 = 5/4

⇒ v = 20/30 × 60 = 40

⇒ 4 unit = 40

⇒ 1 unit = 10

⇒ v + u = 50, v = 40, 

⇒ u = 10

Time = 15/v - u = 15/30 = 1/2

∴ The correct answer is 1/2.

Alternate MethodGiven:

Speed of the boat downstream is 125% of the speed in still water.

Time to cover 20 km in still water = 30 minutes.

Distance to cover upstream = 15 km.

Concept Used:

Speed = Distance / Time

Downstream speed = Speed in still water + Speed of stream

Upstream speed = Speed in still water - Speed of stream

Calculation:

Speed in still water = Distance / Time

⇒ Speed in still water = 20 km / 0.5 hours = 40 km/h

Downstream speed = 125% of speed in still water

⇒ Downstream speed = 1.25 × 40 = 50 km/h

Speed of stream = Downstream speed - Speed in still water

⇒ Speed of stream = 50 - 40 = 10 km/h

Upstream speed = Speed in still water - Speed of stream

⇒ Upstream speed = 40 - 10 = 30 km/h

Time = Distance / Upstream speed

⇒ Time = 15 km / 30 km/h = 0.5 hours = 1/2

∴ The boat will take 0.5 hours to cover 15 km upstream.

Answer: 2) 1/2

Let the speed of the boat in still water be x km/hr

Speed downstream = (x + 5) km/hr

Speed upstream = (x − 5) km/hr

Distance of downstream = Distance of Upstream

∴ (x + 5) × 0.8 = (x − 5) × 1.6

⇒ 0.8x + 4 = 1.6x – 8

⇒ 0.8x = 12 km/hr

⇒ x = 15 km/hr

Given:

Total distance = 144 km

Time taken by rower to go upstream = 12 hours

Time taken by rower to go downstream = 9 hours

Concept used:

Upstream speed = (U - V)

Downstream speed = (U + V)

Speed of stream = (Downstream - Upstream)/2 

Speed = distance/time

Calculation:

Upstream speed of rover = (U - V) = 144/12 = 12 km/h

Downstream speed of rover = (U + V) = 144/9 = 16 km/h

Speed of stream = (16 - 12)/2 = 4/2 = 2 km/h

∴ The correct answer is 2 km/h.

Given:

The speed of the boat in still water = 9 km/h

Concept used:

If the speed of a boat in still water is x km/h and the speed of the stream is y km/h, then

Downstream speed = (x + y) km/h

Upstream speed = (x - y) km/h

Time = Distance/Speed

Calculation:

Let, the speed of the water = x km/h

Time to cover 44 km downstream = 44/(9 + x)

Time to cover 35 km upstream = 35/(9 - x)

so, [44/(9 + x)] + [35/(9 - x)] = 9

⇒ \(\frac{44(9-x)+35(9+x)}{81-x^2}=9\)

⇒ 396 - 44x + 315 + 35x = 729 - 9x²

⇒ 9x2 - 9x - 18 = 0

⇒ x2 - x - 2 = 0

⇒ x2 - 2x + x - 2 = 0

⇒ x (x - 2) + 1 (x - 2) = 0

⇒ (x + 1) (x - 2) = 0

⇒ x + 1 = 0 ⇒ x = - 1  ["-" is neglacted]

⇒ x - 2 = 0 ⇒ x = 2

∴ The speed of the water = 2 km/h

So, time is taken to row 33 km downstream and 28 km upstream = [33/(9 + 2)] + [28/(9 - 2)]

= (33/11) + (28/7)

= 3 + 4 = 7 hours

∴ The boatman will take 7 hours to row 33 km downstream and 28 km upstream

Shortcut TrickHere we can see that, 

The Downstream distance in both cases (44 km & 33 km) are divisible by 11

The Upstream distance in both cases (35 km & 28 km) are divisible by 7.

We can say that because the time required (Number of hours) is a complete number in both cases. (9 hrs & all options are complete numbers not in decimal)

Here, according to the question, 

x = 9 km/hr.

⇒ 44/(9 + y) + 35/(9 - y) = 9 hrs

Put y = 2, so that 9 + y will be 11 & 9 - y = 7

⇒ 44/11 + 35/7 = 4 + 5 = 9

y = 2 satisfies the given equation,

Now, 

⇒ 33/(9 + y) + 28/(9 - y) = 33/(9 + 2) + 28/(9 - 2)  

⇒ 33/11 + 28/7 = 3 + 4 = 7 hrs

∴ The boatman will take 7 hours to row 33 km downstream and 28 km upstream