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Math Class VIII 1 Question Bank
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1. A can do a piece of work in 15 days while B can do it in 10 days.
How long will they take together to do it ?
Ans. A’s 1 day work = 1
15, B’s 1 day work =
1
10
(A + B)’s 1 day work 1 1 2 3 5 1
15 10 10 30 6
+= + = = =
A and B together can do it in 6 days.
2. A, B and C can do a piece of work in 12 days, 15 days and 10
days respectively. In what time will they all together finish it ?
Ans. A’s 1 day work 1
12= , B’s 1 day work
1
15=
C’s 1 day work = 1
10
∴ (A + B + C)’ 1 day work
1 1 1 5 4 6 15 1
12 15 10 60 60 4
+ += + + = = =
Hence, A, B and C will all together finish it in 4 days.
3. A and B together can do a piece of work in 35 days while A alone
can do it in 60 days. How long would B alone take to do it ?
Ans. (A + B)’ 1 day work 1
35=
A’s 1 day work 1
60=
4TIME -WORK AND
TIME-DISTANCE
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B’s 1 day work 1 1 12 – 7 5 1
–35 60 420 420 84
= = = =
Hence, B can alone take to do it in 84 days.
4. A can do a piece of work in 20 days while B can do it in 15 days
with the help of C, they finish the work in 5 days. In what time
would C alone do it ?
Ans. A’s 1 day work 1
20= , B’s 1 day work
1
15=
(A + B)’s 1 day work1 1
20 15= +
3 4
60
+=
7
60=
(A + B + C)’s 1 day work 1
5=
C’s one day work1 7 12 – 7 5 1
–5 60 60 60 12
= = = =
C can alone do the work in 12 days.
5. X can do a work in 15 days and Y in 20 days. If they together work
on it for 4 days ; what fraction of the work will be left ?
Ans. X’s 1 day work 1
15= , Y’s 1 day work
1
20=
(X + Y)’s 1 day work 1 1
15 20= +
4 3 7
60 60
+= =
(X + Y)’s 4 days work 7 7
460 15
= × =
Hence, Remaining work = 7 15 – 7
1 –15 15
= 8
15= .
6. A can do a work in 6 days and B can do it in 8 days. They worked
together for 2 days and then B left the work. How many days will
A require to finish work ?
Ans. A’s 1days work 1
6= , B’s 1 day work
1
8=
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(A + B)’s 1day work 1 1
6 8= +
4 3 7
24 24
+= =
Thus, (A + B)’s 2 days work 7 7
224 12
= × =
∴ Remaining work 7
1–12
= 12 – 7 5
12 12= =
∴ A can do complete work in 6 days
∴ A can do 5
12work in
56
12× days
5
2= days
12
2= days
Hence, A will finish the work in 1
22
days.
7. A can do a piece of work in 40 days. He works at it for 8 days and
then B finishes the remaining work in 16 days. How long will
they take to complete the work if they do it together ?
Ans. A’s, 1day work 1
40=
A’s, 8 days work 8 1
40 5= =
∴ Remaining work 1
1 –5
= 5 –1 4
5 5= =
∵ B can do 4
5 piece of work in 16 days
∴ B’s 1 day work
4
4 15
16 5 16 20= = =
×
Thus, (A + B)’s 1 day work 1 1
40 20= +
1 2 3
40 40
+= =
Math Class VIII 4 Question Bank
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Hence, (A + B) can do a pice of work in
1
3
40
=
days 40
3=
113
3= days
8. If 3 women or 5 girls take 17 days to complete a piece of work,
how long will 7 women and 11 girls working together take to
complete the work ?
Ans. Work done by 3 women = Work done by 5 girls
∴ Work done by 1 woman = Work done by 5
3 girls
∴ Work done by 7 women and 11 girls = work done by
3511
3
+
girls i.e.,
68
3 girls.
Since, 5 girls can do the work in 17 days
∴ 1 girl can do the work in 17 × 5 days
∴
68
3 girls can do the work in
17 5
68
3
×
days 17 5 3
68
× ×= days =
15 3days 3 days
4 4=
Hence, 7 women and 11 girls can the complete the work
in 3
34
days
9. A and B working together can mow a field in 56 days and with the
help of C, they could have mowed it in 42 days. How long would
C take by himself ?
Ans. (A + B)’s 1 day work = 1
56
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(A + B +C)’s 1 day work 1
42=
Thus, C’s 1 day work 1 1
–42 56
= 4 – 3
168=
1
168=
Hence, C can do the work in 168 days.
10. A can do a piece of work in 24 days, A and B can do it in 16 days
and A, B and C in 2
103
days. In how many days can A and C do it ?
A’s 1 day work =1
24
(A + B)’s 1 day work 1
16=
(A + B + C) can do a piece of work in 2 32
10 days days3 3
=
(A + B + C)’s 1 day work 3
32=
∴ C’s 1 day work 3 1
–32 16
= 3 – 2 1
32 32= =
(A + C)’s 1 day work 1 1
24 32= +
4 3 7
96 96
+= =
Hence, (A + C) can do the work in 96
7days
513
7= days.
11. A can do 1
4of a work in 5 days and B can do
1
3of the same in 10
days. Find the number of days in which both working together
will complete the work.
Math Class VIII 6 Question Bank
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Ans. ∴ A can do 1
4 of work in 5 days
∴ A can do 1 work in 5 × 4 days = 20 days
A’s 1 day work = 1
20
∴ B can do 1
3of work in 10 days
∴ B can do 1 work in 10 × 3 days = 30 days
B’s days work 1
30=
∴ (A + B)’s 1 day work 1 1
20 30= +
3 2 5 1
60 60 12
+= = =
Hence, A and B working together will complete the work in 12
days.
12. A and B can do a piece of work in 40 days; B and C in 30 days;
and C and A in 24 days.
(i) How long will it take them to do the work together ?
(ii) In what time can each finish it working alone ?
Ans. (A + B)’s 1 day work 1
40=
(B + C)’s 1 day work 1
30=
(C + A)’s 1 day work 1
24=
(i) [(A + B) + (B + C) + (C + A)]’s i.e. 2(A + B + C)’s 1 day work
1 1 1
40 30 24= + +
3 4 5
120
+ +=
12 1
120 10= = .
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∴ (A + B + C)’s 1 day work 1 1 1
10 2 20= × =
∴ (A + B + C) can do the work in 20 days
(ii) A’s 1 day work 1 1
–20 30
= 3 – 2 1
60 60= =
∴ A can do the work in 60 days
B’s 1 day work 1 1
–20 24
= 6 – 5 1
120 120= =
∴ B can do the work in 120 days
C’s 1 day work 1 1
–20 40
= 2 –1 1
40 40= =
∴ C can do the work in 40 days.
Hence, A, B and C can finish the work in 60 days, 120 days
and 40 days respectively.
13. Mona can make a quilt in 6 days, Sonia in 10 days and Jaya in 15
days. Mona and Sonia work for 3 days. How long will it take
Sonia and Jaya to finish the work ?
Ans. Mona’s 1 day work 1
6=
Sonia’s 1 day work 1
10=
Jaya’s 1 day work 1
15=
(Mona + Sonia)’s 1 day work 1 1
6 10= +
5 3 8 4
30 30 15
+= = =
(Mona + Sonia)’s 3 days work 4 4
315 5
= × =
Remaining part of work 4 5 – 4 1
1 –5 5 5
= = =
Math Class VIII 8 Question Bank
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Now, (Sonia + Jaya)’s 1 day work
1 1 3 2 5 1
10 15 30 30 6
+= + = = =
∴ (Sonia + Jaya) will do a work in 6 days
∴ (Sonia + Jaya) will do the remaining work i.e. 1
5 work in =
6
5 days.
∴ Sonia and Jaya will finish the remaining work in 1
1 days.5
14. A is thrice as good a workman as B and B is twice as good a
workman as C. All the three took up a job and received Rs. 180 as
remuneration. Find the share of each.
Ans. Ratio of work done in one day by each of A and B = 3 : 1
and ratio of work done is one day by each of B and C = 2 : 1
A : B = 3 : 1 or 6 : 2
B : C = 2 : 1
∴ A : B : C = 6 : 2 : 1
Sum of ratios = 6 + 2 + 1 = 9
Total remuneration they received = Rs 180
A’s share = 180 6
20 69
×= × =Rs 120
B’s share = 180 2
20 29
×= × = Rs 40
C’s share =180 1
9
×= Rs 20
15. A can do a certain job in 12 days. B is 60% more efficient than A.
Find the number of days taken by B to finish the job.
Ans. Ratio of time taken by A and B = 160 : 100 = 8 : 5
Let time taken by B to complete the work be x days.
∴ 8 : 5 :: 12 : x ⇒ 8 × x = 5 × 12 ⇒ 5 12
8x
×=
Math Class VIII 9 Question Bank
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⇒15
2x = ⇒
17
2x =
Time taken by B to finish the job = 1
72
days.
16. A is twice as good a workman as B and together they finish a
piece of work in 14 days. In how many days can A alone do it ?
Ans. A’s 1day work : B’s 1 day work = 2 : 1
(A + B)’s 1 day work = 1
14
Divide 1
14in the ratio 2 : 1
Sum of ratios = 2 + 1 = 3
Thus, A’s 1 day work 1 2 1
14 3 21× = .
Hence, A alone can finish the work in 21days.
17. Two pipes A and B can separately fill a tank in 36 minutes and 45
minutes respectively. If both the pipes are opened simultaneously,
how much time will be taken to fill the tank ?
Ans. Part of the tank filled by A in one minute = 1
36
Part of the tank filled by B in one minute = 1
45
Part of the tank filled by A and B in one minute
1 1 5 4 9 1
36 45 180 180 20
+= + = = =
Hence, time taken by A and B to fill the tank = 20 minutes.
18. One tap can fill a cistern in 3 hours and a waste pipe can empty
the full cistern in 5 hours. In what time will the empty cistern be
full, if the tap and the waste pipe are kept open together ?
Ans. Work done by the tap in one hour 1
3=
Math Class VIII 10 Question Bank
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Work done by waste pipe in one hour 1
5=
Net filling in one hour 1 1 5 – 3 2
–3 5 15 15
= = =
Hence, the cistern will be filled in 15
2= hours i.e.
17
2 hours.
19. Two pipes A and B can separately fill a cistern in 20 minutes and
30 minutes respectively,while a third pipe C can empty the full
cistern in 15 minutes. If all the pipes are opened together,in what
time the empty cistern is filled ?
Ans. Cistern filled by A in one minute 1
20=
Cistern filled by B in one minute 1
30=
Cistern filled by (A + B)’s in one minute
1 1 3 2 1
20 30 60 12
+= + = =
C can empty the cistern in one minute 1
15=
Net filling of cisterm one minute 1 1 5 – 4 1
–12 15 60 60
= = =
Hence, the cistern will be filled in 60 minutes i.e., one hour.
20. A tap can fill a tank in 20 hours, while the other can empty it in
30 hours. The tank being empty and if both taps are opened to-
gether, how long will it take for the tank to be half full ?
Ans. Time taken by the tap to fill the tank = 20 hours
∴ In 1 hour tap can fill the tank 1
20=
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∴ Time taken by another tap to empty the tank = 30 hours
∴ In 1 hour tap can empty the tank 1
30=
Net filling in 1 hour 1 1 3 – 2 1
–20 30 60 60
= = =
∴ Tank can be filled in 60 hours. Also, time taken for the tap to
be half full 60 hours
2= = 30 hours.
21. A man takes 150 steps in walking 75 metres. If he takes 3 steps in
1 second, find his speed in (i) m/sec (ii) km/hr.
Ans. Time taken in 3 steps = 1 second
∴ Time taken in 150 steps 1 150
3
×= seconds = 30 seconds
Now in 50 seconds distance covered = 75 m
Thus, distance covered in one second
75 3m m 1.5m
50 2= = =
Speed = 1.5m/sec and speed in km /hr 1.5 60 60
1000
× ×= = 5.4 km /hr.
22. A man covers a distance of 144 km at the speed of 36 km/hr and
another 256 km at the speed of 64 km/hr. Find his average speed
for the whole journey.
Ans. Time taken to cover 144 km at 36 km/hr 144
36= hrs = 4 hrs
Time taken to cover 256 km at 64 km/hr 256
64= hr = 4 hrs
Total distance covered = (144 + 256) = 400 km
Math Class VIII 12 Question Bank
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Total time taken = (4 + 4) hrs = 8 hrs
Hence, Average speed total distance
total time=
400
8= km/hr = 50 km/hr.
23. A car finish a certain journey in 10 hours at a speed of 48 km/hr.
By how much the speed of the car must be increased to cover the
same distance in 8 hours ?
Ans. Time = 10 hours, Speed = 48 km/hr
Distance = speed × time = (48 ×10) km = 480 km
Now, time = 8 hours, Distance = 480 km
∴ Speed 480
8= km/ hr = 60 km/hr
Hence, required increased speed = (60 – 48) km/hr = 12 km/hr.
24. A bus covers a certain distance in 50 minutes, if it runs at a speed
of 54 km/hr. What must be the speed of the bus in order to reduce
the time of journey to 40 minutes ?
Ans. Case I
Speed of the bus = 54 km/hr.
∴ Distance covered in 50 minutes 54 50
4560
×= = km.
Case II
Distance of 45 km covered in = 40 minutes
Hence, speed Distance 45
= 60Time 40
= × km/hr
135 1
km/hr 67 km/hr.2 2
= = = 67.5 km /hr
25. A train covers first 200 km in 1
32
hours and next 100 km in
11
2hours. Find its average speed.
Math Class VIII 13 Question Bank
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Ans. Total time taken for the whole journey 1
32
= hours +1
12
hours
7
2= hours +
3
2 hours
10
2= hours = 5 hours
Total distance covered for the whole journey
= 200 km + 100 km = 300 km.
Hence, Average speed Total Distance
=Total time
300=
5km/hr = 60 km/hr
26. A train travels at 10 km/hr for 2 hours and at 13 km/hr for 1 hour:
Find its average speed.
Ans. Distance covered for 2 hours at the speed 10 km/hr = Speed × time
= 10 × 2 km = 20 km
Distance covered for 1 hour at the speed 13 km/hr
= Speed × time
= 13 × 1 km = 13 km
Total distance covered for the whole journey
= 20 km + 13 km = 33 km
Total time taken for the whole journey
= 2 hours + 1 hours = 3 hours
Hence, Average speed total distance
=total time
33 km= 11km/hr
3 hours=
27. A bus covers 160 km at a speed of 40 km/hr and the next 120 km
at a speed of 60 km/hr. Find its average speed.
Ans. Time taken to cover first 160 km at a speed of 40 km/hr
Distance 160km4hrs
Speed 40km/hr= = =
Math Class VIII 14 Question Bank
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Time taken to cover next 120 km at a speed of 60 km/hr
120km2hrs
60km/hr= =
Total distance covered for the whole journey = 160 km + 120 km
= 280 km
Total time taken for the whole journey = 4 hrs + 2 hrs = 6 hrs
Hence, Average speed Totaldistance
=Total time
280km 140= km / hrs
6 hrs 3=
246 km/hr
3=
28. A bus completes a journey of 420 km in 1
62
hours. The first 3
4
part of the journey was performed at 63 km/hr . Calculate its
speed for the rest of the journey.
Ans. Total journey covered by bus = 420 km
Total time taken 1
62
= = 13
2hours
3
4of journey =
3420× 315
4= km
Speed = 63 km/hr
∴ Time taken to cover 315 km 315
563
= = hours
∴ Remaining journey = 420 – 315 = 105 km
Remaining time 13 3
– 52 2
= = hours
Math Class VIII 15 Question Bank
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Speed of bus distance 105 2
time taken 3
×= = km/hr
Hence, Speed for the rest of journey is 70 km/hr
29. A car completed a journey in 7 hours. One third of the journey
was performed at 20 km/hr and the rest at 30 km/hr. Find the total
length of the journey.
Ans. Let total journey be x km. 1
3rd journey
3
x= km
∴ Time taken to cover 1
rd3
= journey at the speed of 20 km/hr
1
3 20
x= ×
60
x= hours
and remaining journey 1 2
–3 3
x x x= =
Time taken 2
3x km journey if the speed of 30 km/hr
2 1
3 30 45
xx= × = hours
According to the given condition 760 45
x x= + =
⇒3 4
7180
x x+= ⇒
77
180
x=
⇒7 180
1807
x×
= =
Hence, total journey is 180 km
30. A cyclist covered a certain distance in 1
32
hours. The speed for
first half of the distance was 15 km/hr and for the second half it
was 20 km/hr. Find the total distance covered by him.
Math Class VIII 16 Question Bank
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Ans. Let the total distance be x
Distance of 1
2of the journey
2
x= km
Speed during this journey = 15 km/hr
Time taken to cover this journey 2
15
x=
2 15
x=
×hrs
30
x= hrs.
Now, distance of 1
2of the journey
2
x= km
Speed during this journey = 20 km/hr.
Time taken to cover this journey 2
20
x
= hr 2 20
x=
×hrs
40
x= hrs
∴
13
30 40 2
x x+ =
⇒4 3 7
120 2
x x+= ⇒
7 7
120 2
x=
⇒7 120
2 7x
×=
×
⇒ x = 60.
Hence, total distance covered is 60 km.
31. One train is 200 m long and is travelling at a speed of 40 km/hr.
Another train is 300 m long and is travelling at a speed of 60 km/
hr. How much time will they take to go past each other com-
pletely if.
(i) they are running in opposite direction (on parallel tracks)
(ii) they are running in same direction (on parallel tracks)
Ans. To pass each other, distance covered = Sum of lengths of both trains
= (200 + 300) m = 500 m
Math Class VIII 17 Question Bank
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(i) When the trains are travelling in opposite direction, relative speed
= (40 + 60) km/hr = 100 km/hr.
1001000
3600
= ×
m/sec 250
9= m/sec
Time taken by the trains to pass each other
= time taken to cover 500 m at the speed 250
9= m/sec.
500 500 9
sec sec250 250
9
×= =
= 18 sec
(ii) When the trains are travelling in the same direction, relative
speed = (60 –40) km /hr = 20 km /hr
20 1000
3600
×= m/sec
200
36= m/sec
50
9= m/sec
Time taken by the trains to pass each other = time taken to
cover 500 m at the speed 50
9= m/sec.
500 500 9sec 90 sec.
50 50
9
×= = =
32. A train 180 m long passes a telegraph post in 12 seconds. find :
(i) its speed in km/hr,
(ii) the time taken by it to pass a platform 135m long.
Ans. Length of the train = 180m
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i.e. distance = 180 m =180
1000km =
18
100km
Time taken = 12 sec = 12
60 60×
hr = 1
300hr
(i) Speed of the train = distance
time
= 18×300
100×1km/hr = 54 km/hr.
(ii) Here, distance = (180 + 135)m = 315m
= 315
km1000
Speed = 54 km/hr
Time taken to pass the platform = distance 315
hrspeed 1000 54
=
×
= 315 60 60
1000 54
× ×
×sec = 21sec.
33. A train 700 m long is running at 72km/hr. If it crosses a tunnel in
one minute, find the length of the tunnel.
Ans. Length of the tunnel be x km
Length of the train = 700m = 700 7
km km1000 10
=
Here, distance = 7
10x
+
km 10 7
10
x += km
Speed of the train = 72km/hr
Time taken to cross the tunnel = 1minute = 1
60hr
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Hence, speed of train = distance
speed⇒72 =
(10 7)60
10 1
x +
×
⇒ 72 = (10x + 7) 6 2
⇒ 10x + 7 = 72
6⇒ 10x + 7 = 12
⇒ 10x = 12 – 7 ⇒ 10x = 5 ⇒ 5 1
10 2x = =
∴ Length of tunnel = 1 1
km 1000m 500m.2 2
= × =
34. A train, 225m in length, crosses a man standing on a platform in 10
seconds and a bridge in 28 seconds. find :
(i) the speed of the train in km/hr and
(ii) the length of the bridge.
Ans. Length of the train = 225m
(i) Here, distance = 225m = 225
1000km
Time = 10seconds = 10
60×60hr
∴ Speed of the train = distance
time
= 225×60×60
1000 10×km/hr = 81 km/hr.
(ii) Let length of the bridge be x m
Here, distance = (225 + x) = 225
1000
x+
km
Time = 28 seconds = 28
60 60×hr
Math Class VIII 20 Question Bank
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Speed of the train = 81 km/hr
Speed = distance
time
⇒ 81 = (225 )60 60
1000 28
x+ ×
×
⇒ 81 = (225 )36
280
x+
⇒ (225 )36
81280
x+= ⇒ 225 + x =
81 280
36
×
⇒ 225 + x = 630
⇒ x = 630 – 225 = 405
Hence, length of the bridge is 405 m.
35. A and B are two trains of lengths 250 m and 200 m respectively.
They are running on parallel rails at 45km/hr and 36km/hr re-
spectively in opposite directions. In how much time will they be
clear of each other from the moment they meet ?
Ans. Relative speed of the trains = (45 + 36) km/hr = 81 km/hr
Here, distance = (250 + 200) m = 450 m =450
1000km
Hence, time taken by trains to pass each other
= distance 450
hrspeed 1000 81
=
×
= 450 60 60
1000 81
× ×
×
sec = 20 sec.
36. A and B are two trains of lengths 160 m and 140 m. They are
running on parallel rails in the same direction at 72 km/hr and
27km/hr respectively. In how much time will A pass B completely,
from the moment they meet ?
Ans. Relative speed of the train = (72 – 27)km/hr = 45km/hr
Thus, distance = (160 + 140) m
Math Class VIII 21 Question Bank
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= 300 m =300
1000km
Hence, time taken by the trains to pass each other
= distance 300
speed 1000 45=
×
hr
= 300 60 60
1000 45
× ×
×second = 24 second
37. Rohan cycles to his office at the rate of 1
122
km/hr and is late by 3
minutes, However, if he travels at 15 km/hr, he reaches 5 minutes
earlier than the usual time. What is the distance of his office from
his residence ?
Ans. Let total distance be x km
In first case, speed = 1
122
km/hr = 25
2 km /hr
∴ Time taken = 2
25
x ×
hrs = 2
25
xhrs
In second case, speed = 15 km/hr
∴ Time taken = 15
xhrs
According to the given condition
2 3 5–
25 15 60
x x +=
⇒2 2
–25 15 15
x x=
⇒6 – 5 2
75 15=
x x ⇒ x = 10
Hence, total distance is 10 km
Math Class VIII 22 Question Bank
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38. Robert is travelling on his cycle and has calculated to reach point A
at 2 P. M. if he travels at 10 km/hr. However, he will reach there at
12 noon if he travels at 15 km/hr. At what speed must he travel to
reach A at 1 P.M. ?
Ans. Case I
Speed = 10 km/hr and In second case speed = 15 km/hr
Let distance be x km
∴ Time in first case = 10
xhrs and time taken in second case
= 15
xhrs
Difference in time = 2P.M – 12 Noon = 2 hrs
∴ According to the given condition – 210 15
x x=
⇒ 3 – 2
230
x x= ⇒ 2
30
x= ⇒ x = 60
∴ Total distance = 60 km
Now time taken in first case = 60
610
= hours
and time taken in second case = 60
415
= hours
Now time = 5 hours and distance = 60 km
∴ Hence,distance 60
speed of Robert = 12time 5
= = km/hr
39. A stream is flowing at 3 km/hr. A boat with a speed of 10 km/hr in
still water is rowed upstream for 13 hours. Find the distance rowed
How long will it take to return to the starting point ?
Ans. Speed upstream = (10 – 3) km/hr = 7km/hr
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Time taken = 13 hrs
∴ Distance covered = speed × time = 7 × 13 km = 91 km
distance = 91 km
Speed back i.e. downstream = (10 + 3) km/hr = 13 km/hr
Hence, time taken to return to the starting point
= Distance
speed =
91
13hrs = 7 hrs
40. The rate of current in a river is 2.5 km/hr . A boat with a speed
9.5km/hr in still water is rowed downstream for 7 hours. Find
the distance rowed . How long will it take to return to the starting
point ?
Ans. Speed downstream = (9.5 + 2.5) km/hr = 12 km/hr
Time taken = 7 hrs
Thus, distance rowed = speed × time = 12 × 7 = 84 km
Now distance = 84 km
Speed to back i.e. upstream = (9.5 – 2.5) = 7 km/hr
Hence, time to return to the starting point = distance
speed
84
7= hrs = 12 hrs
41. The speed of a boat in still water is 10km/hr. It is rowed upstream
for a distance of 45 km in 6 hours. Find the speed of the stream.
Ans. Let speed of the stream be x km/hr.
Speed upstream = (10 – x) km/hr
Distance covered = 45 km
Time taken = 6 hrs
Speed = distance
time
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⇒45
10 –6
x = ⇒ 6 (10 – x) = 45
⇒ 60 – 6x = 45 ⇒ 60 – 45 = 6x
⇒ 15 = 6x ⇒ 6x = 15
⇒15
6x = ⇒ x = 2.5
Hence, speed of the stream is 2.5 km/hr.
42. A stream is flowing at 4.8 km/hr. A boat is rowed downstream for
a distance of 49 km in 1
32
hours. Find the speed of the boat in
still water.
Ans. Let speed of the boat in still water be x km/hr
Speed downstream = (x + 4.8) km/hr
Distance covered = 49 km
Time taken = 1
32
hr = 7
2hrs
Thus, distance
speed of boat =time
⇒ x + 4.8 = 49 2
7
×
⇒ x + 4.8 = 14
⇒ x = 14 – 4.8 ⇒ x = 9.2
Hence, speed of the boat in still water is 9.2 km/hr.
43. The speed of a boat in still water is 6 km/hr. If the boat covers a
distance of 22.5 km downstream in 3 hours find the speed of the
current.
Ans. Speed of boat downstream = distance
time =
22.5km7.5 km/hr
3hours =
But speed of boat down stream = Speed of boat in still
water + Speed of the current
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Thus, current speed = Speed of boat downstrem – speed of boat in
still water
= 7.5 km/hr – 6 km/hr = 1.5 km/hr
44. A stream is flowing at 3 km/hr. A boat with a speed of 9 km/hr is
rowed downstream for 1
32
hours. Find the distance covered. How
long will it take to return to the starting point ?
Ans. Speed of boat in still water = 9 km/hr
Speed of stream = 3 km/hr
Relative speed of the boat with the stream = (9 + 3) km/hr = 12 km/
hr
Distance covered by the boat = distance covered by the boat with
the speed 12 km/hr in 1
32
hours = 1
12×32
km = 7
12×2
km = 42 km
When boat is return, then it speed is against the stream.
Now, relative speed of the boat against the stream
= (9 – 3) km/hr = 6 km/hr
Time taken by the boat to return to the starting point = time taken
by the boat to cover 42 km at the speed 6 km/hr
= 42km
76 km/hr
= hours.
45. The speed of a boat in still water is 9 km/hr. If the boat goes 54
km down stream in 4 hours; find the speed of the stream
Ans. Let speed of the stream be x km/hr. Speed of the boat downstream
(x + 9) km/hr
According the given condition = 54
4+ 9x
=
⇒ 4 (x + 9) = 54 ⇒ 4x + 36 = 54
⇒ 4x = 54 – 36 ⇒ 4x = 18
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⇒ 18
4x = ⇒ x = 4.5
Hence, speed of the stream is 4.5 km/hr
46. The speed of a boat downstream is 16 km/hr and its speed upstream
is 10 km/hr. Find the speed of the boat in still water and the rate of
the stream.
Ans. Speed of boat down stream = 16 km/h and speed upstream = 10 km/h
Let the speed of boat in still water be x km/h and
Speed of stream be y km/hr
∴ x + y = 16 …(i)
x – y = 10 …(ii)
Adding (i) and (ii) we have
2x = 26 ⇒ x = 13
substituting the value of x in (i) we have
13 + y = 16 ⇒ y = 16 – 13 ⇒ y = 3
Hence, speed of boat in still water = 13 km/hr and of stream = 3
km/hr
47. A boat can be rowed with the stream at 15 km/hr and against the
stream at 12 km/hr. What is the speed of the stream ?
Ans. Let the speed of boat be x km/hr and speed of stream be y = km/hr
Then speed of boat with the stream be = (x + y) km/hr
According to the given condition
x – y = 15 …(ii)
Also, speed of boat against the stream = (x – y) km/hr
According to the given condition
x + y = 12 …(ii)
Adding (i) and (ii), we have
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15
– 12
2 27
x y
x y
x
+ =
=
=
⇒ 27
13.52
x = =
Substituting the value of x in equation (i) we have
13.5 + y = 15
⇒ y = 15 – 13.5
⇒ y = 1.5
Hence, speed of stream is 1.5 km/hr.
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