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# Time and Distance Questions for IBPS PO Prelims

Question 1:Â Places A and are 45 km apart from each other. A car starts from place A and another car starts from place at the same time. If they move in the same direction, they meet in 4 and a half hour and if they move towardseach other, they meet in 27 minutes. Whatis the speed (in km/h) of the car which moves faster?

a)Â 56

b)Â 55

c)Â 45

d)Â 50

Question 2:Â A boat can cover 336 km distance downstream in 4.2 hours. The same boat can cover the same distance in still water in 6.72 hours. Find out the speed of the stream.

a)Â 35 km/h

b)Â 25 km/h

c)Â 40 km/h

d)Â 30 km/h

Solution:

The same boat can cover the same distance in still water in 6.72 hours.
Speed of the boat in still water = $\frac{336}{6.72}$ = 50 km/h
A boat can cover 336 km distance downstream in 4.2 hours.
$\frac{336}{50 + \text{speed of the stream}} = 4.2$
80 = 50 + speed of the stream
speed of the stream = 80-50 = 30 km/h
Hence, option d is the correct answer.

Question 3:Â Find the average speed of a car traveling at 12km/hr for 40km and the same distance at 15km/hr?

a)Â $\dfrac {40}{3}$ km/hr

b)Â $\dfrac {20}{3}$ km/hr

c)Â $\dfrac {25}{3}$ km/hr

d)Â None of the above

Solution:

The average speed covered by the car traveling the same distance for two speeds let x and y is given as
= 2xy/(x+y)
= $\dfrac {(2 \times 12 \times 15)}{12+15}$
= $\dfrac {360}{27}$
= $\dfrac {40}{3}$ km/hr

Question 4:Â A boat covers a 20 km distance towards downstream in 4 hours. If the speed of the boat is 1.5 times the speed of the current then find the time taken by the boat to cover the same distance in upstream.

a)Â 22 hours

b)Â 20 hours

c)Â 25 hours

d)Â Canâ€™t be determined

Solution:

Let the speed of the boat and speed of the stream be x km/hr and y km/hr respectively.
ATQ,
Distance = Speed x Time
Upstream speed = x-y
Downstream speed = x+y
20 = 4(x+y)
x+y = 5
Given x=1.5y,
So,
1.5y + y = 5
2.5y = 5
y = 2km/hr
x = 3 km/hr

Time taken to cover 20 km in upstream, let it be â€˜Tâ€™
20 = T(x-y)
20 = T x 1
T = 20 hours

Question 5:Â One pipe P can fill a tank in 24 hours. Two pipes Q and R with equal efficiency are opened along with P and hence the tank is filled in 12 hours. Find the time taken by R alone to fill the complete tank alone.

a)Â 36 hours

b)Â 32 hours

c)Â 48 hours

d)Â 24 hours

Solution:

Time taken by P alone to fill the tank = 24 hours
Time taken by P, Q and R to fill the tank = 12 hours.
Let the capacity of the tank be 48 units.
Efficiency of P = $\dfrac{48}{24}$ = 2 units per hour
Efficiency of P, Q and R together = $\dfrac{48}{12} = 4$ units per hour.
Efficiency of Q and R together = 4-2 = 2 units per hour.
Hence, Efficiency of Q and R = 1 unit per hour each.
Therefore, R can fill the tank in $\dfrac{48}{1} = 48$ hours.

Question 6:Â The ratio between the speed of bus and truck is 6:7 respectively. A bus can cover d km distance in 7 hours. A truck can cover (d-140) km distance in 5 hours. Then find out the value of d.

a)Â 840

b)Â 700

c)Â 660

d)Â 980

Solution:

The ratio between the speed of bus and truck is 6:7 respectively.
Let’s assume the speed of bus and truck is 6y and 7y respectively.
A bus can cover d km distance in 7 hours.
$\frac{d}{7} = 6y$

$\frac{d}{42} = y$ Eq.(i)

A truck can cover (d-140) km distance in 5 hours.
$\frac{(d-140)}{5} = 7y$

$\frac{(d-140)}{35} = y$ Eq.(ii)

Equating Eq.(i) and Eq.(ii).
$\frac{(d-140)}{35} = \frac{d}{42}$

$\frac{(d-140)}{5} = \frac{d}{6}$

6d – 840 = 5d
6d-5d = 840
d = 840 km
Hence, option a is the correct answer.

Question 7:Â A boat can cover 720 km distance downstream in 40 hours. The speed of boat in still water is double the speed of the stream. Then find out the time taken by boat to cover 480 km distance in upstream.

a)Â 100 hours

b)Â 60 hours

c)Â 40 hours

d)Â 80 hours

Solution:

Let’s assume the speed of boat in still water and the speed of stream is B and C respectively.
A boat can cover 720 km distance downstream in 40 hours.
B+C = $\frac{720}{40}$

B+C = 18 km/h Eq.(i)
The speed of boat in still water is double the speed of stream.
B = 2C Eq.(ii)
Put Eq.(ii) in Eq.(i).
2C+C = 18 km/h
3C = 18 km/h
C = 6 km/h Eq.(iii)
Put Eq.(iii) in Eq.(ii).
B = $2\times6$ = 12 km/h
The time taken by boat to cover 480 km distance in upstream = $\frac{480}{B-C}$
= $\frac{480}{12-6}$

= $\frac{480}{6}$

= 80 hours
Hence, option d is the correct answer.

Question 8:Â Pipe P and pipe Q together can fill a tank in 31.5 hours. Pipe R alone can empty the tank in 63 hours. Find out the time taken by all the three pipes together to fill 33.33% of the tank.

a)Â 35 hours

b)Â 28 hours

c)Â 42 hours

d)Â 21 hours

Solution:

Letâ€™s assume the total capacity of the tank is 504.
Pipe P and pipe Q together can fill a tank in 31.5 hours.
Efficiency of pipe P and Q together = 504/31.5 = 16
Pipe R alone can empty the tank in 63 hours.
Efficiency of pipe R = 504/63 = – 8 (Here negative sign is for emptying the tank.)
33.33% of the tank = â…“ of 504 = 168
Time taken by three pipes together to fill the tank = 168/(16-8) = 168/8 = 21 hours
Hence, option d is the correct answer.

Question 9:Â The time taken by the pipes A and B together to fill the tank is 30% of the time taken by the pipe C alone to fill the same tank. The time taken by pipeÂ A alone to fill the same tank is 4 hours more than the time taken by pipeÂ B alone to fill the tank. If the time taken by pipeÂ A alone to fill the tank is 12 hours, then find the time taken by pipeÂ C alone to fill the tank.

a)Â 8 hours

b)Â 16 hours

c)Â 12 hours

d)Â 10 hours

Solution:

Time taken by A to fill the tank alone = 12 hours.
Then, Time taken by B alone to fill the tank = 12-4 = 8 hours.
Let the capacity of the tank be 48 units (LCM of 12 and 8).
Efficiency of A = 4 units per hour.
Efficiency of B = 6 units per hour.
Time taken by A and B together to fill the tank = $\dfrac{48}{4+6} = \dfrac{48}{10} = 4.8$ units per hour.
Then, Time taken by C alone to fill the tank = $\dfrac{4.8}{30\%} = 16$ hours.

Question 10:Â A boat can cover 390 km distance upstream in 78 hours. The speed of the stream is 44.44% of the speed of the boat. Then find out the time taken by boat to cover the same distance downstream.

a)Â 30 hours

b)Â 35 hours

c)Â 25 hours

d)Â 20 hours

Solution:

Letâ€™s assume the speed of the boat in still water is B and the speed of the stream is C.
The speed of the stream is 44.44% of the speed of the boat.
C = 44.44% of B
$C = \frac{4}{9}\times B$ Eq.(i)
A boat can cover 390 km distance upstream in 78 hours.
$\frac{390}{78} = B – C$
B – C = 5 Eq.(ii)
Put Eq.(i) in Eq.(ii).
$B – \frac{4}{9}\times B = 5$

$\frac{5}{9}\times B = 5$
B = 9 km/h Eq.(iii)
Put Eq.(iii) in Eq.(ii).
9 – C = 5
C = 9 – 5 = 4 km/h
Time taken by boat to cover the same distance downstream = $\frac{390}{9+4}$
= $\frac{390}{13}$

= 30 hours
Hence, option a is the correct answer.

Question 11:Â Three pipes A, C and B can fill a tank in 12 hours, 24 hours and 18 hours respectively. If in the first hour, A and B are opened and in the second hour, A and C are opened and in the third hour, all three pipes are opened and this process is repeated till the tank is filled, then how much time does it take to fill the tank?

a)Â 8.46 hours

b)Â 6.8 hours

c)Â 9.42 hours

d)Â 8.48 hours

Solution:

Let the total capacity of the tank be 72 units (LCM of 12, 24 and 18).
Efficiency of A = $\dfrac{72}{12} = 6$ units.
Efficiency of B = $\dfrac{72}{18} = 4$ units.
Efficiency of C = $\dfrac{72}{24} = 3$ units.

A and B are opened in the first hour, A and C are opened in the second hour, A, B and C are opened in the third hour.
Then, in three hours, 6+4+6+3+6+4+3 = 32 units of the tank will be filled.
Then, 64 units of the tank will be filled in 6 hours.
Remaining 8 units of the tank will be filled by A and B together in $\dfrac{8}{10} = 0.8$ hours.

Hence, The tank will be filled in 6+0.8 = 6.8 hours.

Question 12:Â Pipes P and Q can fill the tank together in 11.52 hours. Pipes Q and R can fill the tank together in 19.2 hours. Pipes P and R can fill the tank together in $13\dfrac{1}{11}$ hours. Find the time taken by all the three pipes to fill the tank together.

a)Â 9.29 hours

b)Â 10.67 hours

c)Â 8.33 hours

d)Â 9.84 hours

Solution:

Pipes P and Q can fill the tank together in 11.52 hours.
P+Q â†’ 11.52 = $\dfrac{288}{25}$ units.
Pipes Q and R can fill the tank together in 19.2 hours.
Q+R â†’ 19.2 = $\dfrac{96}{5}$ or $\dfrac{288}{15}$ units.
Pipes P and R can fill the tank together in $13\dfrac{1}{11}$
P+R â†’ $\dfrac{144}{11}$ or $\dfrac{288}{22}$ units.

Let the total capacity of the tank be 288 units.
Efficiency of P+Q = 25 units.
Efficiency of Q+R = 15 units.
Efficiency of P+R = 22 units.
Efficiency of 2(P+Q+R) = 62 units.

Efficiency of P+Q+R = 31 units.

Hence, The tank will be filled by P, Q and R together in $\dfrac{288}{31} = 9.29$ hours.

Question 13:Â Pipe A and B can together fill a tank in 12 hours and pipe B and C can together fill a tank in 15 hours. If the efficiency of A is two times that of C, then find the time taken by Pipe B alone to fill the tank completely.

a)Â 16.33 hours

b)Â 24.5 hours

c)Â 20 hours

d)Â 13 hours

Solution:

According to the question,
Let the total work = (LCM 12,15) = 60
Efficiency of A + B = 60/12 = 5 units per hour
Efficiency of B + C = 60/15 = 4 units per hour
Efficiency of A = 2 $\times$ efficiency of C
Efficiency of A = 5 – efficiency of B —— eq 1
Efficiency of C = 4 – efficiency of B
Efficiency of A = 8 – 2 $\times$ efficiency of B —— eq 2

Now on comparing both the equation 1 and 2, we get
5 – efficiency of B = 8 – 2 $\times$ efficiency of B
Efficiency of B = 3 units per hour
So,
Time taken by B to fill the tank = 60/3 = 20 hours.

Question 14:Â If the man can row 800m in 20 minutes against the current of the river, and returns the same distance in 10 minutes , then find the speed of man and speed of the river respectively.

a)Â 1, $\frac{1}{3}$ m/s

b)Â 3, 5 m/s

c)Â 2, $\frac{1}{2}$ m/s

d)Â None of the above

Solution:

According to the question,
Let the speed of the man be m, and the speed of the river be b
On rowing against the current,
m – b = $\frac{800}{20\times 60} = \frac{2}{3}$
On rowing downstream,
m + b = $\frac{800}{10\times 60} = \frac{4}{3}$

On solving this we get,
2m = 2, m = 1m/s
b = $\frac{1}{3}$ m/s

Question 15:Â Two cars each from point X and Y respectively start travelling with the constant speed, where the distance between point X and Y is 150km then find the speed of the car with greater speed, given that if the cars move in the same direction they must meet in 6 hours and if they move towards each other then they must meet after 120 minutes.

a)Â 40 km/h

b)Â 45 km/h

c)Â 35 km/h

d)Â 50 km/h

Solution:

According to the question,
Distance = 150 km
Let the speed of the car starting from point X be x km/hr
And Y be y km/hr
When moving is same direction,
x – y = 150/6 , x – y = 25
When moving towards each other
x + y = 150/2, x + y = 75
Solving this we get,
2x = 100, x = 50 km/hr
y = 25km/hr