Question

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Answer 1

Answer:

20 days - Option(3).

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!

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.