Question

A can do a work in three days whereas B can do the same work in five days and C in ten days. Find the time taken by all three to do the work in one day.

Answer 1

The correct answer is 30/19 days.

A can do a work in 3 days

B can do a work in 5 days

C can do a work in 10 days

Take LCM of 3,5,10 which is 30

So the total unit of work is 30

Means A can do 30/3 = 10 units per day

B can do 30/5 = 6 units per day

C can do 30/10 = 3 units per day

Now A + B + C = 19 units per day

So Total = 30/19 days

Answer 2

Given:-

A can do a work in three days whereas B can do the same work in five days and C in ten days. Find the time taken by all three to do the work in one day.

To Find:-

Find the time taken by all three to do the work in one day.

Solution:-

Let B alone finish the work =X days

And alone finish the work =(x-10) days

A's one day work =$\frac{1}{x - 10}$

B's one day work =$\frac{1}{x}$

As it given the (A+B)can finish work in 12days

∴(A+B)one day work=$\frac{1}{12}$

=>A's someday work+B's Someday work=$\frac{1}{12}$

$= > \frac{1}{x - 10} + \frac{1}{x} = \frac{1}{12} \\ = > \frac{x + x - 10}{x(x - 10)} = \frac{1}{12} \\ \frac{2x - 10}{x(x - 10)} = \frac{1}{12} \\ = > 12(2x - 10) = x(x - 10) \\ = > 24x - 120 = {x}^{2} - 10x \\ = > {x}^{2} - 10x - 24x + 120 = 0 \\ = > {x}^{2} - 34x + 120 = 0 \\ {x}^{2} - 30x - 4x + 120 = 0 \\ x(x - 30) - 4(x - 30) = 0 \\ (x - 4)(x - 30) = 0$

=>x=for x =30

X is not equal to 4

∴if x=40

Then A alone can finish the work in =(4-10)

=-6days

which is not possible

∴x=30days

∴B Alone can finish work in 30days

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