Question
A takes 6 days less than the time taken by B to finish a piece of work. If both A and B together can finish it in 4 days, find the time taken by B alone to finish the work.
Answer: Option C
:
C
Suppose B alone can takesx days to finish the work.
Then A alone can finish it in (x−6) days.
B's 1 day's work = 1x.
A's 1 day's work = 1x−6.
(A+B)'s 1 day's work = 14
∴1x+1x−6=14
⇒x−6+xx(x−6)=14
⇒8x−24=x2−6x
⇒x2−14x+24=0
⇒x2−12x−2x+24=0
⇒(x−12)(x−2)=0
⇒x=12orx=2
But x cannot be less than 6.
⇒x=12
Hence, B alone can finish the work in 12 days
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:
C
Suppose B alone can takesx days to finish the work.
Then A alone can finish it in (x−6) days.
B's 1 day's work = 1x.
A's 1 day's work = 1x−6.
(A+B)'s 1 day's work = 14
∴1x+1x−6=14
⇒x−6+xx(x−6)=14
⇒8x−24=x2−6x
⇒x2−14x+24=0
⇒x2−12x−2x+24=0
⇒(x−12)(x−2)=0
⇒x=12orx=2
But x cannot be less than 6.
⇒x=12
Hence, B alone can finish the work in 12 days
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