Question

A, b and c can do a work separately in 16, 32 and 48 days respectively. they started the work together but b leaving off 8 days and c six days before the completion of the work. in what time is the work finished?

Answer 1

A B C
Done: 16 32 48
Can : x x-8 x-6
Work = done/can
X/16+(x-8)/32+(x-6)/48=1
Lcm is 96
6x+3x-24+2x-12/96=1
So x=12days... So work will be completed after 12 days

Answer 2

Answer: The work is finished in 12 days.

Step-by-step explanation:

Let the work done by A in x days.

Let the work done by B in x-8 days.

Let the work done by C in x-6 days.

Since we have given that

Number of days in which A can finish his work = 16 days

Number of days in which B can finish his work = 32 days

Number of days in which C can finish his work = 48 days

According to question,

$\frac{x}{16}+\frac{x-8}{32}+\frac{x-6}{48}=1\\\\L.C.M.\ of\ 16,32,48=96\\\\\frac{4x+3(x-8)+2(x-6)}{96}=1\\\\6x+3x-24+2x-12=96\\\\11x-36=96\\\\11x=96+36\\\\11x=132\\\\x=\frac{132}{11}\\\\x=12$

Hence, the work is finished in 12 days.