Question

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 ?​

Answer 1

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.

Answer 2

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.