Question

a, b, and c can do a piece of work in 20, 24 and 30 days, respectively. They undertook to do the piece of work for ₹5400. They begin the work together but b left 2 days before the complete of work and c left 5 days before the completion of work. The share a from the assured money is-

Answer 1

see let the total work done by them of
lcm(20,24,30)=120 units
it means a can 120/20=6 units work in one day
similarly b can do 5 units and c will do 4 units in one day
when c leaves the work
a will work for 5 more days whiche means 30 units of work
b will work for 3 more days which means 15 units of work
it means a b c will work togather for 75 units of work which means 75/15=5 days togather
a will do 30 units in 5 days
b will do 25 units in 5 days
c will do 20 units in 5 days
total work done by a=30+30=60 units
b does 40(25+15) units
c does 20 units
they did work in the ratio 60:40:20 or 3:2:1
now 3x+2x+x=5400
or x=900
so a will charge 2700 rs b 1800 and c 900 rs
ask any doubt if arised