Question

9 A and B together complete a piece of work in T days.A alone completes the work in T+3
days and B alone completes the piece of work in T+12 days what is T?
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Answer 1

Given :

• A and B together complete a piece of work in T days.
• and A alone completes the same work in T+3 days.
• also B alone completes the same work in T+12 days.

To Find :

The value of T.

Solution :

Let the total work is = 1

$Efficiency=\dfrac{Work}{Time}$

∵ A and B together take T days to complete the work.

 ∴ $A+B=\dfrac{1}{T}$

∵ and A alone take T+3 days to complete the work.

∴  $A=\dfrac{1}{T+3}$

∵ also B alone take T+12 days to complete the work.

∴  $B=\dfrac{1}{T+12}$

Now, according to the question,

$\dfrac{1}{T+3}+\dfrac{1}{T+12}=\dfrac{1}{T}$

(T+3)(T+12) = T( 2T+15)

$T^{2}$ + 15T + 36 = 2$T^{2}$ + 15T

$T^{2}$ = 36

∴T = 6

The value of T is 6.