Up and Down Both MCQ Quiz - Objective Question with Answer for Up and Down Both - Download Free PDF
Last updated on May 22, 2025
Latest Up and Down Both MCQ Objective Questions
Up and Down Both Question 1:
A boat can covers a certain distance in upstream and same distance in downstream in total of 7 hours 48 minutes, If upstream speed of the boat is 62.5%. of downstream speed of the boat and speed of the stream is 3 km/h, what is the total distance covered by the boat?
Answer (Detailed Solution Below)
Up and Down Both Question 1 Detailed Solution
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
Up and Down Both Question 2:
A boat can covers a certain distance in upstream and same distance in downstream in total of 7 hours 48 minutes, If upstream speed of the boat is 62.5%. of downstream speed of the boat and speed of the stream is 3 km/h, what is the total distance covered by the boat?
Answer (Detailed Solution Below)
Up and Down Both Question 2 Detailed Solution
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
Up and Down Both Question 3:
The speed of a stream is 8 km/h. A boat can go 19 km downstream and 9 km upstream in 4 hours. What is the speed (in km/h) of the boat in still water?
Answer (Detailed Solution Below)
Up and Down Both Question 3 Detailed Solution
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
Up and Down Both Question 4:
A boat travels at a speed of 12 km/h in still water. If the speed of the stream is 4 km/h, find the time taken by the boat to travel 112 km downstream.
Answer (Detailed Solution Below)
Up and Down Both Question 4 Detailed Solution
Given:
Speed of the boat in still water = 12 km/h.
Speed of the stream = 4 km/h.
Distance to be travelled downstream = 112 km.
Formula Used:
Time taken = Distance / Speed
Calculation:
Speed downstream = Speed of the boat in still water + Speed of the stream
Speed downstream = 12 km/h + 4 km/h
Speed downstream = 16 km/h
Time taken = Distance / Speed downstream
Time taken = 112 km / 16 km/h
⇒ Time taken = 7 hours
The time taken by the boat to travel 112 km downstream is 7 hours.
Up and Down Both Question 5:
The speed of a boat in still water is 24 km/hr, and the speed of the stream is 6 km/hr. If the speed of the stream decreases by 50% and the speed of the boat decreases by 25%, what will be the time taken by the boat to travel 63 km downstream?
Answer (Detailed Solution Below)
Up and Down Both Question 5 Detailed Solution
Speed of the boat in still water = 24 km/hr
Speed of the stream = 6 km/hr
Speed of the stream decreases by 50%:
New speed of stream = 6 - (0.5 × 6) = 3 km/hr
Speed of the boat decreases by 25%:
New speed of boat = 24 - (0.25 × 24) = 18 km/hr
Downstream speed is the sum of the boat's speed and the stream's speed:
Downstream speed = Speed of boat + Speed of stream = 18 + 3 = 21 km/hr
Time is calculated using the formula:
Time = Distance / Speed = 63 / 21 =3 hours
So, the total time is 3 hours.
Top Up and Down Both MCQ Objective Questions
A boat goes 20 km upstream and 44 km downstream in 8 hours. In 5 hours, it goes 15 km upstream and 22 km downstream. Determine the speed of the boat in still water.
Answer (Detailed Solution Below)
Up and Down Both Question 6 Detailed Solution
Download Solution PDFConcept 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
A man rows a boat a certain distance downstream in 9 hours, while it takes 18 hours to row the same distance upstream. How many hours will it take him to row three-fifth of the same distance in still water?
Answer (Detailed Solution Below)
Up and Down Both Question 7 Detailed Solution
Download Solution PDFGiven:
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 (3/5th of 180km) 108 km in 108/15 = 7.2 hr
A swimmer swims from a 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. If the distance between P and Q is 120 m then the speed of the current (in km/h) is:
Answer (Detailed Solution Below)
Up and Down Both Question 8 Detailed Solution
Download Solution PDFGiven:
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.
A motorboat whose speed is 20 km/h in still water takes 30 minutes more to go 24 km upstream than to cover the same distance downstream. If the speed of the boat in still water is increased by 2 km/h, then how much time will it take to go 39 km downstream and 30 km upstream?
Answer (Detailed Solution Below)
Up and Down Both Question 9 Detailed Solution
Download Solution PDFGiven:
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
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. What is the speed (in km/h, to the nearest integer) of the boat in still water?
Answer (Detailed Solution Below)
Up and Down Both Question 10 Detailed Solution
Download Solution PDFGiven:
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
A man can row a distance of 8 km downstream in a certain time and can row 6 km upstream in the same time. If he rows 24 km upstream and the same distance downstream in \(1\frac{3}{4}\) hours, then the speed (in km/h) of the current is:
Answer (Detailed Solution Below)
Up and Down Both Question 11 Detailed Solution
Download Solution PDFGiven:
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
The speed of a boat down the stream is 125% of the speed in still water. If the boat takes 30 minutes to cover 20 km in still water, then how much time (in hours) will it take to cover 15 km upstream?
Answer (Detailed Solution Below)
Up and Down Both Question 12 Detailed Solution
Download Solution PDFGiven :
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
A boat covers a certain distance downstream in 0.8 hour, while it comes back in 1.6 hour. If the speed of the stream be 5 km/hr, what is the speed of the boat in still water?
Answer (Detailed Solution Below)
Up and Down Both Question 13 Detailed Solution
Download Solution PDFLet 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
A boatman can row his boat in still water at a speed of 9 km/h. He can also row 44 km downstream and 35 km upstream in 9 hours. How much time (in hours) will he take to row 33 km downstream and 28 km upstream?
Answer (Detailed Solution Below)
Up and Down Both Question 14 Detailed Solution
Download Solution PDFGiven:
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
To go a distance of 144 km upstream, a rower takes 12 hours while it takes her only 9 hours to row the same distance downstream. What is the speed of the stream?
Answer (Detailed Solution Below)
Up and Down Both Question 15 Detailed Solution
Download Solution PDFGiven:
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.