A and B can do a piece of work in 72 days; B and C can do it in 120 da

Question

A and B can do a piece of work in 72 days; B and C can do it in 120 days; A and C can do it in 90 days. In what time can A alone do it?

(A) 150 days 
(B) 120 days
(C) 100 days 
(D) 80 days
(E) 70 days

Nidzo · Accepted Answer

Make each of the joint rates out of 360

1/a + 1/b = 1/72 -> 1/a + 1/b = 5/360  (1)

1/b + 1/c = 1/120 -> 1/b + 1/c = 3/360  (2)

1/a + 1/c = 1/90 -> 1/a + 1/c = 4/360  (3)

(1) - (2) =   1/a - 1/c = 2/360  (4)

(4) + (3) =   2/a = 6/360

6a = 720
a = 120

Answer B.

Sorry  Bunuel  Answer choices D and E are repeats

Bunuel · Answer

________________
Fixed. Thank you.

LipiSinha · Answer

Total units of work = 360

1 day work of A+B = 5 units
1 day work of B+C = 3 units
1 day work of A+C = 4 units

So, 1 day work of A+B+C = 6 units (Add the above and divide by 2)

Since, A, B and C together finish 6 units of work in 1 day and B and C together finish 3 units of work in 1 day, A alone will complete 3 units of work in 1 day.

Hence, A will take 120 days ( \frac{360}{3} ) to finish the work alone.

The answer will be B.

ScottTargetTestPrep · Answer

Solution:
 
If we let a, b, and c be the number of days it takes A, B, and C to each complete the work alone, respectively, we can create the equation:

1/a+ 1/b = 1/72, 1/b + 1/c = 1/120, and 1/a + 1/c = 1/90

If we add the three equations, we have:

2/a + 2/b + 2/c = 1/30

1/a + 1/b + 1/c = 1/60

Now subtract 1/b + 1/c = 1/120 from 1/a + 1/b + 1/c = 1/60, we have:

1/a = 1/120

a = 120

Answer: B

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A and B can do a piece of work in 72 days; B and C can do it in 120 da

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A and B can do a piece of work in 72 days; B and C can do it in 120 da

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