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A takes 15 days more time taken by B to finish a work. A and B can together complete the work in 10 days. In how many days A alone can finish the work?
- A15
- B45
- C30
- D40
Answer not set
Discussion 1
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CCommunity
Let, B can finish the work in = x days
∴ A can finish the work in = (x + 15) days
∴ B’s 1 day’s work = 1/x
∴ A’s 1 day’s work = 1/(x + 15)
(A + B) can complete the work in = 10 days
∴ (A + B)’s 1 day’s work = 1/10
According to problem,
⇒ 1/x + 1/(x + 15) = 1/10
⇒ (x + 15 + x)/(x (x + 15)) = 1/10
⇒ x2 + 15x = 20x + 150
⇒ x2 - 5x - 150 = 0
⇒ x2 - 15x + 10x - 150 = 0
⇒ x (x - 15) + 10(x - 15) = 0
⇒ (x - 15) (x + 10) = 0
⇒ x = 15 or -10
∴ B can finish the work in = 15 days [cannot be negative]
∴ A can finish the work in = (15 + 15) = 30 days
∴ A can finish the work in = (x + 15) days
∴ B’s 1 day’s work = 1/x
∴ A’s 1 day’s work = 1/(x + 15)
(A + B) can complete the work in = 10 days
∴ (A + B)’s 1 day’s work = 1/10
According to problem,
⇒ 1/x + 1/(x + 15) = 1/10
⇒ (x + 15 + x)/(x (x + 15)) = 1/10
⇒ x2 + 15x = 20x + 150
⇒ x2 - 5x - 150 = 0
⇒ x2 - 15x + 10x - 150 = 0
⇒ x (x - 15) + 10(x - 15) = 0
⇒ (x - 15) (x + 10) = 0
⇒ x = 15 or -10
∴ B can finish the work in = 15 days [cannot be negative]
∴ A can finish the work in = (15 + 15) = 30 days