6. A and B together can complete a
piece of work in 72 days, B and
C together can complete it in 120
days, and A and C together in 90
days. In what time can A alone
complete the work ?
Answers
Answer :-
A alone can complete the work in 40 days.
Explanation :-
A and B can complete a work in 72 days
So, A and B's 1 day work (A + B) = 1/72
B and C can complete it in 120 days
So, B and C's 1 day work (B + C) = 1/120
A and C can complete it in 90 days
So, A and C's 1 day work (A + C) = 1/90
By Observation :
2(A + B + C) = (A + B) + (B + C) + (A + C)
By substituting the values
⇒ 2(A + B + C) = (1/72) + (1/120) + (1/90)
Taking LCM
⇒ 2(A + B + C) = (5 + 3 + 4)/360
⇒ 2(A + B + C) = 12/360
⇒ 2(A + B + C) = 1/30
⇒ A + B + C = 1/(30 * 2)
⇒ A + B + C = 1/60
We know that
A = (A + B + C) - (B + C)
By substituting the values
⇒ A = (1/60) - (1/120)
Taking LCM
⇒ A = (2 + 1)/120
⇒ A = 3/120
⇒ A = 1/40
i.e A's 1 day work = 1/40
⇒ A can complete it in 40 days
∴ A alone can complete the work in 40 days.
Solution
According to question given we know that A and B together can complete a
piece of work in 72 days, B and
C together can complete it in 120
days, and A and C together in 90
days and we have to find what time can A alone complete the work.
Hence
1 / 72 = ( A + B ) for 1 day work.
1 / 120 = ( B + C ) for 1 day work.
1 / 90 = ( C + A ) for 1 day work.
2 ( A + B + C ) = ( A + B ) + ( B + C ) + ( A + C )
= 2 ( A + B + C ) = 1 / 7 + 1 / 120 + 1 /90
(LCM Taking)
= 2 ( A + B + C ) = (5 + 3 + 4) / 360
= 2 ( A + B + C) = 120 / 360
= 2 ( A + B + C) = 1 / 30
= A + B + C = 1 / 30 +
= A + B + C = 1 / 60
Hence
A = ( A + B + C ) - ( B + C )
A = 1 / 60 - 1 / 120
Again Taking LCM
A = ( 2 + 1 ) / 120
A = 3 / 120
A = 1 / 40
A = 40
Hence, 40 days is time can A alone complete the work.