Question

3 Men, A, B, and C complete a work in such a way that A works for all the day. B works for 1st and 2nd day and C works for 3rd, 4th and 5th day. If B+C can do as much work in 2 days as A alone does in 3 days. In how many days A, B and C alone do the work If B+C can complete the whole work without the help of A in 6 days ?
Please solve this question by short trick

Answer 1

Answer:

A can complete the work in 9 days

B can complete the work in 18 days

C can complete the work in 9 days

Step-by-step explanation:

B and C can do as much work in 2 days as A does in 3 days (Given)

∵ B and C finish a work in 6 days (Note: 2 multiplied by 3 = 6)

∴ A alone can finish the work in 9 days ( 3 multiplied by 3)

Let work done by B in one day is $x$ and work done by C in one day is $y$

Work done by A in one day = $\frac{1}{9}$

According to the question

$\frac{5}{9}+2x+3y =1$

or, $2x+3y=1-\frac{5}{9}$

or, $2x+3y=\frac{4}{9}$                  ........ (i)

Again, since B and C can complete the work in 6 days

∴ $6x+6y=1$

or, $x+y=\frac{1}{6}$                     ............(ii)

Multiplying eq (ii) by 2 and subtracting it from eq (i)

$y = \frac{4}{9} -\frac{1}{3}$

or, $y=\frac{1}{9}$

Putting the value of y in eq (ii)

$x+\frac{1}{9} = \frac{1}{6}$

or, $x=\frac{1}{6} -\frac{1}{9}$

or, $x=\frac{1}{18}$

Thus, in 1 day B completes $\frac{1}{18}$ work

Therefore, B can complete the work in 18 days

Similarly, C can complete the work in 9 days (∵ in 1  day C does $\frac{1}{9}$ work)

Hence,

A can complete the work in 9 days

B can complete the work in 18 days

C can complete the work in 9 days

Answer 2

Answer:

3 3/5

Step-by-step explanation:

Step 1:

1. AB

2.AB

3.AC

4.AC

5.AC.

Step 2 : Time Efficiency

A 3 2

_______ = __ = __

B + C 2 3

Step 3:

Given,

B and c can together complete the work in 6days without the help of A

So,

Total work = 6 * 3 = 18

From step 1

We get

5A +2(B+C)+ C = 18

10+ 6 +C = 18

C=2

A:B:C

2:1:2

So, 18/5 = 3 3/5