A and B together can do a piece of work in 12 days, B and C together can do it in 15 days, whereas C and A together can do it in 20 days. in how many days will they finish the work, working together?
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Let AA requires XX days, BB requires YY days and CC requires ZZ days,
In one day,
A will do 1X1X of the total workB will do 1Y1Y of the total workC will do 1Z1Z of the total work
Since, A & B will do the work in 1212 days, in one day they will do 112112of the work
this implies,
1X+1Y=1121X+1Y=112 (1)
similarly get the other equations
1Y+1Z=1151Y+1Z=115 (2)
1X+1Z=1201X+1Z=120 (3)
(1)−(2)+(3)(1)−(2)+(3)
2X=112−115+1202X=112−115+120
2X=1152X=115
1X=1301X=130
X=30X=30 days
If you want you can figure out others as well!
Hope it Helps!
In one day,
A will do 1X1X of the total workB will do 1Y1Y of the total workC will do 1Z1Z of the total work
Since, A & B will do the work in 1212 days, in one day they will do 112112of the work
this implies,
1X+1Y=1121X+1Y=112 (1)
similarly get the other equations
1Y+1Z=1151Y+1Z=115 (2)
1X+1Z=1201X+1Z=120 (3)
(1)−(2)+(3)(1)−(2)+(3)
2X=112−115+1202X=112−115+120
2X=1152X=115
1X=1301X=130
X=30X=30 days
If you want you can figure out others as well!
Hope it Helps!
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