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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

Best Answer 

 #1
avatar+730 
+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.

 


laugh

 Apr 30, 2021
 #1
avatar+730 
+2
Best Answer

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.

 


laugh

MathProblemSolver101 Apr 30, 2021
 #2
avatar+121000 
0

Impressive,  MPS   !!!!!!

 

 

 

cool cool cool

CPhill  Apr 30, 2021

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