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

+= =

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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.

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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

×=

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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=

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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

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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.

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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= = =

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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

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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.

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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

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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

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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

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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

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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.