 # Time and Work ( 16 to 20 )

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Time and Work ( 16 to 20 ):

# APTITUDE QUESTIONS (TIME AND WORK):

16. P can do a piece of work in 10 days; Q in 15 days. They work for 5 days. The rest of the work was finished by R in 2 days. If they get Rs. 1500 for the whole work, the daily wages of Q and R are:

A)    Rs. 150

B)    Rs. 225

C)    Rs. 250

D)    Rs. 300

E) None of these

Explanation:

Part of the work done by P = (1/10* 5)= 1/2
Part of the work done by Q = (1/15* 5)= 1/3
Part of the work done by R = 1- (1/2+ 1/3) = 1/6
So, (P’s share) : (Q’s share) : (Z’s share) = 1/2 : 1/3 : 1/6 =3:2:1
∴ P’s share = Rs. (3/6* 1500) = Rs. 750, Q’s share = Rs. (2/6* 1500) = Rs. 500, R’s share = Rs. (1/6* 1500) = Rs. 250
P’s daily wages = Rs. (750/5) = Rs. 150, Q’s daily wages = Rs. (500/5) = Rs. 100, R’s daily wages = Rs. (250/5) = Rs. 125
∴ daily wages of Q and R = Rs. (100 + 125) = Rs.225

17. C alone can complete a work in 16 days and D alone in 12 days. Starting with C, they work on alternate days. The total work will be completed in:

A)    12 days

B)    13 days

C)    13(5/7) days

D)    13(3/4) days

E)    None of these

Explanation:

(C+D)’s 2 day’s work = (1/16+ 1/12) = 7/48
Work done in 6 pairs of days = (7/48* 6) = 7/8 . Remaining work = (1- 7/8) = 1/8
Work done by C on 13th day = 1/16, remaining work = (1/8- 1/16) = 1/16
On 14th day, it is D’s turn.
1/12 work is done D in 1 day, 1/16 work is done by D in (12* 1/16) = 3/4 day.
∴ Total time taken = 13(3/4) days

18. Twenty women can do a work in 16 days. 16 men can complete the same work in 15 days. What is the ratio between the capacity of a man and a woman?

A)    5:4

B)    4:3

C)    5:3

D)    3:4

E) None of these

Explanation:

(20 * 16) women can complete the work in 1 day.
∴ 1 women’s 1 day’s work = 1/320
(16 *15) men can complete the work in 1 day
∴ 1 man’s 1 day’s work = 1/240
So, required ratio = 1/240 ∶ 1/320 = 4:3

19. 12 men can complete a work in 9 days. After working for 6 days, 6 more men join them. In how many days the work will get complete?

A)    2 days

B)    5 days

C)    6 days

D)    4 days

E)    None of these

Explanation:

1 man’s 1 day’s work = 1/108
12 men’s 6 day’s work = (1/9* 6) = 2/3, remaining work = (1- 2/3) = 1/3
18 men’s 1 day’s work = (1/108* 18) = 1/6
1/6 work is done by them in 1 day
∴ 1/3 work is done by them in (6* 1/3) = 2 days.

20. A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. For 1 man and 1 woman how many boys will be required to assist them to complete the job in 1/4 of a day?

A)    1

B)    4

C)    19

D)    41

E)    None of these

Explanation:

(1 man + 1 woman)’s 1 day’s work = (1/3+ 1/4)= 7/12
Work done by 1 man and 1 woman in 1/4 day = (7/12* 1/4) = 7/48
Remaining work = (1- 7/48) = 41/48
Work done by 1 boy in 1/4 day = (1/12* 1/4) = 1/48
∴ number of boys required = (41/48* 48) = 41