Algebra-A-B-together-can-finish-a-work-in-24-days-B-C-in-30-days-If-C-is-20-more-efficient-than-B-then-how-many-days-are-required-for-A-alone-to-finish-the-work-

Tinku Tara June 3, 2023 Algebra 0 Comments

Question Number 135354 by liberty last updated on 12/Mar/21

Algebra A & B together can finish a work in 24 days, B & C in 30 days. If C is 20% more efficient than B, then how many days are required for A alone to finish the work?

A l g e b r a

A & B together can finish a work in 24 days, B & C in 30 days. If C is 20% more efficient than B, then how many days are required for A alone to finish the work?

Answered by EDWIN88 last updated on 12/Mar/21

(1) A&B ⇒Work = 24(V_A +V_B ) ⇒(W/(24)) = V_A +V_B ...(i) (2) B&C⇒ Work= 30(V_B +V_C ) , where V_C =(6/5)V_B ⇒ ((Work)/(30)) = ((11)/5) V_B ⇒V_B = (W/(66))...(ii) ⇒V_A = (W/(24))−(W/(66)) = ((7W)/(264)) ; so many days for A alone to finish is = ((264)/7) ≈ 37.714 days

(1) A & B \Rightarrow Work = 24 (V_{A} + V_{B})

\Rightarrow \frac{W}{24} = V_{A} + V_{B} \dots (i)

(2) B & C \Rightarrow Work = 30 (V_{B} + V_{C}), where V_{C} = \frac{6}{5} V_{B}

\Rightarrow \frac{Work}{30} = \frac{11}{5} V_{B} \Rightarrow V_{B} = \frac{W}{66} \dots (ii)

\Rightarrow V_{A} = \frac{W}{24} - \frac{W}{66} = \frac{7 W}{264}; so many days for

A alone to finish is = \frac{264}{7} \approx 37.714 days

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