if A can do a piece of work in 4 hours. B and C together 3 hours and A and C together in 2 hours, then B alone take to do it is
Answers
Answer:
Let a,b & c be the number of days taken by A, B & C to complete the work alone.
Given, A can do a piece of work in four hours.
=> 1/a = 1/4——————(1)
B and C together can do it in 3 hours,
=> 1/b + 1/c = 1/3———-(2)
A and C together can do it in 2 hours,
=> 1/a + 1/c = 1/2———-(3)
Using (1) & (3)
1/c = 1/2 - 1/4 = 1/4——-(4)
Using (2) & (4)
1/b = 1/3 - 1/4 = 1/12
=> b = 12
=> The number of days taken by B to complete the work alone is 12 hours.
If A can do the work (W) alone in 4 hours, then he can do 1/4 W per hour, or 1/2 W in 2 hours. Therefore, if A and C do the work in 2 hours, then A does 1/2 of the work in that time, and C also does 1/2 W in the 2 hours (i.e., A and C each do half of the work in the 2 hours). If C does 1/2 W in two hours, then he does half of that (1/4) in one hour. So C does 1/4 W per hour, and in 3 hours does 3/4 W. So if C and B take three hours to do the work, C is doing 3/4 of the work and B is doing only 1/4 of the work in that three hours. So in one hour, he can only do 1/3 of the 1/4 that it took him three hours to do. That is, in one hour B can do 1/4 of 1/3 W, which is 1/12 W. If B can only do 1/12 of W in one hour, then it will take him 12 hours to complete the work alone.
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Amount of work A does in 1 h = (1/4) <= A takes 4 h to complete a piece of work.
Amt of work B and C can complete in 1 h = (1/3) <= B and C take 3 h to complete a piece of work.
Amt of work A and C can complete in 1 h = (1/2) <= A and C take 2 h to complete a piece of work.
Rewriting as equations : A + C = 1/2, B + C = 1/3, A = 1/4
A + C = 1/2 => 1/4 + C = 1/2 => C = 1/2 - 1/4 = 1/4 ie C takes 4 h to complete a piece of work.
B + C = 1/3 => B + 1/4 = 1/3 => B = 1/3 - 1/4 = 1/12 ie B takes 12 h to complete a piece of work.
OR
A + C = 1/2, B + C = 1/3 => (A + C) - (B + C) = 1/2 - 1/3
A - B = 1/2 - 1/3 = 1/6
1/4 - B = 1/6
B = 1/4 - 1/6 = 1/12 ie B takes 12 h to complete a piece of work.
A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will C alone take to do it?
A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in how many days?
If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days what is time taken by 15 men and 20 boys?
Let Total Work = LCM(2,3,4) = 12 units.
A does 12/4= 3 units per hour.
A + C complete 12/2 = 6 units per hour.
=> C complete 6 - 3 = 3 units per hour.
B + C complete 12/3 = 4 units per hour.
=> B complete 4 - 3 = 1 unit per hour.
=> B alone can complete work in 12/1 = 12 hours.
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A does 1 work in 4 hours , in 2 hours does 1/2
A+C does 1 work in 2 hours , A does 1/2 , so C does 1/2 in 2 hours .
C does in 2 hours 1/2 work, in 1 hours 1/4 work,
in 3 hours 3/4 work .
B+C does in 3 hours 1 work ,in which C does3/4.
so in 3 hours B does 1–3/4=1/4 work
so B alone does 1 work in 3×4=12 hours . ans
12 hours.
A does the job W in 4 hours, therefore A’s work rate is 0.25 W per hour.
If A and C together do the job in 2 hours, A does 0.5W, and so does C, so both work at 0.25 Wph.
If B and C together take 3 hours, C does 0.75, B does 0.25. So B alone would take 3(0.25) x 4 to do W.
Either B is learning the job, or he’s going to get fired.
A's one hour work= 1/4.
(B+C)’s one hour work = 1/3.
(A+C)’s one hour work=1/2.
Thus C's one hour work = 1/2–1/4=1/4.
And B's one hour work=1/3–1/4= 1/12.
Thus , B can do the same work in 12 hours . Answer.
Step-by-step explanation:
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Answer:
Step 1: A can do a piece of work in 4 hours => In 1 hour, A can complete 1/4 th of the work. (A = 1/4) — equation 1
Step 2: A and C together can do it in 2 hours => In 1 hour, A and C can complete 1/2 of the work. (A+C = 1/2) — equation 2
Step 3: Solving equations 1 and 2, we get C = 1/2 - A = 1/2 - 1/4 = 1//4. C=1/4 means C can complete 1/4th of the work in 1 hour => C can complete the work in 4 hours.
Note: B and C together can do it in 3 hrs is extra/redundant information and is not required to solve this problem.
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