## Time and Work

#### Time and Work

1. A man, on tour travel first 160 km, at 64 km/hr. and the next 160km at 80km/hr. the average speed for the first 320 km. of the tour is ?
1. 35.55km/hr.
2. 71.11km/hr.
3. 36km/hr.
4. 72km/hr.

1. Average speed = 2t1 x t2/( t1 + t2)

##### Correct Option: B

Average speed = 2t1 x t2/( t1 + t2)
= (2x64x80)/(64+80)km
= (2 x 64 x 80 ) / 144 km/hr.
=71.11km/hr.

1. By walking at 3/4 of his usual speed, a man reaches his office 20 minute later than usual. this usual time is ?
1. 30 minute
2. 60 minute
3. 75 minute
4. 1 hour 30 minute

1. At a speed of 3/4 of the usual speed, the time taken is 4/3 of the usual time

##### Correct Option: B

At a speed of 3/4 of the usual speed, the time taken is 4/3 of the usual time
= (4/3 of usual time ) – (usual time ) = 20min.
⇒ 4x/3 -x = 20
⇒ x/3 =20
⇒ x=60 min

1. A man travels 35 km partly at 4 km/hr and at 5 km/hr. If he covers former distance at 5 km/hr and later distance at 4 km/hr, he could cover 2 km more in the same time. The time taken to cover the whole distance at original rate is
1. 9 hours
2. 7 hours
3. 4.5 hours
4. 8 hours

1. Suppose the man covers first distance in x hrs. and second distance in y hrs.

##### Correct Option: D

Suppose the man covers first distance in x hrs. and second distance in y hrs.
Then , 4x + 5y = 35 and 5x +4y= 37
Solving these equation , we get
X=5 and y=3
Total time taken = (5+3) hrs= 8hrs

1. 6 men or 10 women can reap a field in 15 days, then the number of days that 12 men and 5 women will take to reap the same field is :
1. 5
2. 6
3. 8
4. 12

1. Work done by 6 men = work done by 10 women.
Work done by 1 man = work done by 10 / 6 = 5/3 women
∴ 12 men + 5 women = 12 x ( 5 / 3) + 5 = 25 women
∴ W1 x D 1 = W2 x

##### Correct Option: B

Work done by 6 men = work done by 10 women.
Work done by 1 man = work done by 10 / 6 = 5/3 women
∴ 12 men + 5 women = 12 x ( 5 / 3) + 5 = 25 women
∴ W1 x D 1 = W2 x D2 W = women, D=days
10 X 15 = 25 x D2
D2 = 6

1. 6 children and 2 men complete a certain piece of work in 6 days. Each child takes twice the time taken by a man to finish the work. In how many days will 5 men finish the same work?
1. 6
2. 8
3. 9
4. 15

1. 6C + 2M = 6days
36C + 12M = 1 days
Again 1M = 2C
∴ 36+12X2 = 1 day
60 children can do the work in 1 day

##### Correct Option: A

6C + 2M = 6days
36C + 12M = 1 days
Again 1M = 2C
∴ 36+12X2 = 1 day
60 children can do the work in 1 day
Now, 5 men = 10 children
∴ 10 children can do the work in 6 days.