Question

Adam and paul can archive the sales target of the company in 30 days. Paul and charles in 40 days while charles and adam in 60 days . In how many days can all three of them archive the sales target together ?

Answer 1

Given: Adam and Paul can achieve the sales target in 30 days

           Paul and Charles can do that in 40 days

           Charles and Adam can do that in 60 days

To find: Number of days in which they achieve the target when they work together

Solution: Let Adam, Paul and Charles be x, y and z respectively.

Work done by Adam and Paul in 1 day = 1/30

Work done by Paul and Charles in 1 day = 1/40

Work done by Charles and Adam in 1 day = 1/60

Now let us frame the information we know into three equations.

x + y = 1/30 [equation i]

y + z = 1/40 [equation ii]

z + a = 1/60 [equation iii]

Subtracting equation ii from equation i, we get

x - z = 1/30 - 1/40

⇒ x - z = (4 - 3)/120

⇒ x - z = 1/120 [equation iv]

Now adding equations iii and iv, we get

2x = 1/60 + 1/120

⇒ 2x = 3/120

⇒ x = 1/80

Putting the value of x in equation i,

y = 1/30 - 1/80 = 5/240

Putting the value of x in equation iii,

z = 1/60 - 1/80 = 1/240

Now, the work done by x, y and z together in 1 day = 1/80 + 5/240 + 1/240

                                                                                     = (3 + 5 + 1)/240

                                                                                     = 9/240

Therefore, all three of them can complete the task together in = 240/9 days

                                                                                                        = 26.667 days

                                                                                                   = 27 days (approx)

Answer: 27 days

Answer 2

Answer:

All three of them can complete the task together in = 240/9 days =27 days(approx)

Step-by-step explanation:

As per the data given in the question,

We have,

Let work done by adam, paul and charles in one day be $a,p,c$

So, work done by Adam and paul in one day = $\frac{1}{30}$

work done by Paul and charles in one day = $\frac{1}{40}$

work done by charles and adam in one day = $\frac{1}{60}$

So, we have the equations:

$a+p=\frac{1}{30}..............(i) \\p+c=\frac{1}{40}..............(ii) \\c+a=\frac{1}{60}..............(iii)$

So, adding (i)(ii)(iii) we get

$2(a+p+c)=\frac{9}{120}\\(a+p+c)=\frac{9}{240}$

Hence, all three do 9/240 work in one day.

So,all three of them can complete the task together in = 240/9 days =27 days(approx)

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