Three workers can do a job in 6 days. Two of the workers work twice as fast as the third. How long would it take one of the faster workers to do the job himself?
A
15 days
B
18 days
C
24 days
D
12 days
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Question: Three workers can do a job in 6 days. Two of the workers work twice as fast as the third. How long would it take one of the faster workers to do the job himself?
Solution:
Let,
the first and 2nd worker need x days.
Third worker needs 2x days
ATQ,
(1/x) + (1/x) + (1/2x) = 1/6
⇒ (2 + 2 + 1)/2x = 1/6
⇒ 5/2x = 1/6
⇒ 2x = 30
∴ x = 15
So the one faster worker alone will take 15 days to complete the job.
0
Updated: 2 months ago
P and Q can do a job in 3 days. Q and R can do the same job in 4 days, while R and P can do it in 12 days. In how many days the job will be finished when P, Q and R working together.
Created: 2 months ago
A
10 days
B
3 days
C
4 days
D
12 days
Question: P and Q can do a job in 3 days. Q and R can do the same job in 4 days, while R and P can do it in 12 days. In how many days the job will be finished when P, Q and R working together.
Solution:
Given that,
(P + Q)'s 1 day's work = 1/3
(Q + R )'s 1 day's work= 1/4
and
(R + P)'s 1 day's work = 1/12
Now, (P + Q) + (Q + R) + (R + P) = 2(P + Q + R)'s 1 day's work = (1/3) + (1/4) + (1/12)
= (4 + 3 + 1)/12
= 8/12 = 2/3
∴ (P + Q + R)'s 1 day's work = 2/(3 × 2) = 1/3
So, P + Q + R can complete the job in = 3 days
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Updated: 2 months ago
A man can do a work in 20 days and a woman in 15 days. If they work on it together for 5 days, then the fraction of the work that is left-
Created: 2 months ago
A
8/15
B
1/12
C
5/12
D
None of these
Question: A man can do a work in 20 days and a woman in 15 days. If they work on it together for 5 days, then the fraction of the work that is left-
Solution:
Man's 1 day's work = 1/20
Woman's 1 day's work = 1/15
∴ (Man + woman)'s 1 day's work = (1/20) + (1/15) = (3 + 4)/60 = 7/60
∴ (Man + woman)'s 5 day's work = (7/60) × 5 = 7/12
Thus, Remaining work = 1 - (7/12) = (12 - 7)/12 = 5/12
∴ The fraction of the work that is left = 5/12
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Updated: 2 months ago
A can complete a piece of work in 6 days working 8 hours a day, and B can complete the same work in 12 days working 8 hours a day. How long will it take them to complete the work together if they work 4 hours a day?
Created: 2 months ago
A
6 days
B
5 days
C
10 days
D
8 days
Question: A can complete a piece of work in 6 days working 8 hours a day, and B can complete the same work in 12 days working 8 hours a day. How long will it take them to complete the work together if they work 4 hours a day?
Solution:
A can complete the work in 8 × 6 = 48 hours
1 hour's work of A = 1/48 part
B can complete the work in 8 × 12 = 96 hours
1 hour's work of B = 1/96 part
(A + B)'s 1 hour's work = (1/48) + (1/96) part
= (2 + 1)/96 part
= 3/96 part
= 1/32
∴ Time taken by (A + B) working 4 hours daily = 32/(1 × 4)
= 8 days
0
Updated: 2 months ago
