Question

A and B together can complete a task in 1.2 days. However, if A works alone, completes half the job and leaves and
then B works aloe and completes the rest of the work, it takes 2.5 days in all to complete the work. If B is more
efficient than A how many days would it have taken B to do the work by herself?​

Answer 1

Correct Question :- A and B together can complete a task in 12 days. However, if A works alone, completes half the job and leaves and then B works alone and completes the rest of the work, it takes 25 days in all to complete the work. If B is more efficient than A , than how many days would it have taken by B to do the work by herself ?

Solution :-

Let us assume that, A takes x days to complete the work alone and B takes y days to complete the work alone.

given that, both takes 12 days to complete a task together.

So,

→ 1/x + 1/y = 1/12 ----------- Eqn.(1)

Also, given that, if A completes half work alone and B completes rest half they take 25 days.

So,

→ x/2 + y/2 = 25

→ (x + y)/2 = 25

→ x + y = 50

→ x = (50 - y) ------------- Eqn.(2)

Putting value of Eqn.(2) in Eqn.(1) ,

→ 1/(50 - y) + 1/y = 1/12

→ (y + 50 - y) / y(50 - y) = 1/12

→ 50 * 12 = 50y - y²

→ y² - 50y + 600 = 0

→ y² - 30y - 20y + 600 = 0

→ y(y - 30) - 20(y - 30) = 0

→ (y - 30)(y - 20) = 0

Putting both equal to 0, we get,

→ y = 30 and 20.

Now, if y = 30

→ x = 50 - y = 50 - 30 = 20 days .

if y = 20,

→ x = 50 - y = 50 - 20 = 30 days.

Since , B is more efficient than A , she will take lesser time to complete the task.

Hence, B would take 20 days to do the work by herself.

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Answer 2

Step-by-step explanation:

Given that A and B can complete a work in 12 days.

Therefore, 1/A + 1/B =  (1/12)   ---- (i)

According to the given condition,

=> A/2 + B/2 = 25

=> A + B = 50

=> A = 50 - B    ----- (ii)

Substitute (ii) in (i), we get

→ 1/(50 - B) + 1/B = 1/12

→ 12B + 12(-B + 50) = B(-B + 50)

→ -B² + 50B - 600 = 0

→ B² - 50B + 600 = 0

→ B² - 20B - 30B + 600 = 0

→ B(B - 20) - 30(B - 20) = 0

→ (B - 20)(B - 30) = 0

→ B = 20,30

If B = 20:

A = 30

If B = 30:

A = 20.

Given that B is more efficient that A,he will take lesser time to do the job alone. Hence A will take 20 days and A will take 30 days.

Therefore,B will do the work in 20 days.

• Hope it helps you !