Question : A, B, and C can complete a work in 10, 12, and 15 days respectively. They started the work together, but A left the work before five days of its completion. B also left the job two days after A left. In how many days was the work completed?
Option 1: 4 days
Option 2: 5 days
Option 3: 7 days
Option 4: 8 days
Correct Answer: 7 days
Solution :
A left the work 5 days before completion.
B left the work 3 days before completion.
We know that Total work = Number of days × Efficiency of work.
Let the number of days required to complete the whole work = $x$ and the whole work is 1.
1 day work of A = $\frac{1}{10}$
1 day work of B = $\frac{1}{12}$
1 day work of C = $\frac{1}{15}$
According to the question,
$\frac{x-5}{10} + \frac{x-3}{12} + \frac{x}{15} = 1$
$⇒6(x-5)+5(x-3)+4x = 60$
$⇒6x-30+5x-15+4x =60$
$⇒15x-45 = 60$
$⇒15x=105$
$\therefore x=7$
Hence, the correct answer is 7 days.
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