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# Asap plz?

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Two persons A and B together can do a work in 10 days the same work can befinished in 18 days if A works alone for 12 days and B works alone for 6 days,
then
1) The time required for A to finish the work if he work alone is 15 days
2) The time required for B to finish the work if he work alone is 30 days
3) The time required for A to finish the work if he work alone is 20 days
4) The time required for B to finish the work if he work alone is 40 days​

Apr 30, 2021

#1
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Two persons A and B together can do a work in 10 days the same work can be

finished in 18 days if A works alone for 12 days and B works alone for 6 days, then

1) The time required for A to finish the work if he work alone is 15 days

2) The time required for B to finish the work if he work alone is 30 days

3) The time required for A to finish the work if he work alone is 20 days

4) The time required for B to finish the work if he work alone is 40 days

Let a be number of days it takes for person A to finish the work alone.

Let b be number of days it takes for person B to finish the work alone.

Let 1 represent 100% of the job.

We know that 10/a + 10/b = 1. (1)

We also know that 12/a + 6/b = 1. (2)

(1): Multiplying both sides by ab, we have: 10b + 10a = ab (3)

(2): Multiplying both sides by ab, we have: 12b + 6a = ab (4)

(3) = (4): 10b + 10a = 12b + 6a

Dividing both sides by 2, we have: 5b + 5a = 6b + 3a.

Moving and combining like terms to one side, we have b = 2a (5).

Substituting (5) into (1): 10/a + 10/2a = 1.

Multiplying both sides by a we have 10 + 5 = a.

So a=15.

Thus b = 30.

Person A will take 15 days, person B will take 30 days. Apr 30, 2021

#1
+2

Two persons A and B together can do a work in 10 days the same work can be

finished in 18 days if A works alone for 12 days and B works alone for 6 days, then

1) The time required for A to finish the work if he work alone is 15 days

2) The time required for B to finish the work if he work alone is 30 days

3) The time required for A to finish the work if he work alone is 20 days

4) The time required for B to finish the work if he work alone is 40 days

Let a be number of days it takes for person A to finish the work alone.

Let b be number of days it takes for person B to finish the work alone.

Let 1 represent 100% of the job.

We know that 10/a + 10/b = 1. (1)

We also know that 12/a + 6/b = 1. (2)

(1): Multiplying both sides by ab, we have: 10b + 10a = ab (3)

(2): Multiplying both sides by ab, we have: 12b + 6a = ab (4)

(3) = (4): 10b + 10a = 12b + 6a

Dividing both sides by 2, we have: 5b + 5a = 6b + 3a.

Moving and combining like terms to one side, we have b = 2a (5).

Substituting (5) into (1): 10/a + 10/2a = 1.

Multiplying both sides by a we have 10 + 5 = a.

So a=15.

Thus b = 30.

Person A will take 15 days, person B will take 30 days. MathProblemSolver101 Apr 30, 2021
#2
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Impressive,  MPS   !!!!!!   CPhill  Apr 30, 2021