A and B can do a work in 12 days and 27 days more respectively then A and B working together. How long will B take to finish the work alone?
Answers
Given : A and B can do a work in 12 days and 27 days more respectively then A and B working together
To Find : How long will B take to finish the work alone?
40 days
45 days
50 days
55 days
Solution:
Let say A & B can complete the work together in X days
Then A can complete the Work in X + 12 days
Then B can complete work in X + 27 days
Work in 1 day by both = 1/X
work in 1 day by A = 1/(X + 12)
Work in 1 day by B = 1/(X + 27)
=> 1/X = 1/(X + 12) + 1/(X + 27)
=> (X + 12)(X + 27) = X (X + 27) + X(X + 12)
=> X² + 39X + 324 = X² + 27X + X² + 12X
=> 324 = X²
=> X = 18
B can complete work in X + 27 days
=> 18 + 27 = 45 Days
B will take 45 days to finish the work alone.
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Answer:
Let (A + B) can do work in n days.
- A can do = (n + 12) days
- B can do = (n + 27) days
⇒ (A + B)'s work = (A × B) / (A + B)
⇒ n = (n + 12)(n + 27) / (n + 12) + (n + 27)
⇒ n = n² + 39n + 324 / 2n + 39
⇒ n(2n + 39) = n² + 39n + 324
⇒ 2n² + 39n = n² + 39n + 324
⇒ 2n² + 39n - n² - 39n = 324
⇒ n² = 324
- Square Root both sides
⇒ n = 18
• B will finish work alone :
⇢ B = (n + 27) days
⇢ B = (18 + 27) days
⇢ B = 45 days
∴ Hence, Option 2 ) 45 days is correct.