Question

IF A AND B CAN PAINT THE FENCE OF A PARK IN 8 DAYS, B AND C CAN PAINT THE SAME FENCE IN 12 DAYS, AND C AND A CAN FAINT THE FENCE IN 6 DAYS
THEN FIND THAT I HOW MUCH TIME WILL EACH OF THEM WOULD TAKE TO PAINT THE FENCE AND HOW MUCH TIME WOULD THEY TAKE IF ALL OF THEM WORKS TOGETHER TO PAINT THE FENCE

Answer 1

A and B can paint fence in 8 days.
so Total time take by A and B is 1/8 days

B and C can paint fence in 12 days.
so Total time taken by B and C is 1/12 days.

C and A can paint fence in the 6 days.
so Total time taken by B and C is 1/6 days.

if the work together they can complete work in
= 1/8 + 1/12 + 1/6= LCM is 24
=4+2+4/24= 10/24 or 5/12 days.

Answer 2

a+b=8. .....(1)
b+c=12. .....(2)
a+c=6. ......(3)
now,
a+b+2=a+c
=b-c= -2. ......(4)

now, adding equation 2 and 4

2b=10
b=5
now putting B's value in equation 1
a=3

now putting value of b in equation 2
c=7
so together they will do work in
(a×2÷3)+(b×2÷3)+(c×2÷3)
2+(10/3)+(14/3)
2+(24/3)
2+8=10 days
separately,
a=3×2=6
b=5×2=10
c=7×2=14