Question

a b c together can do a piece of work in 15 days B alone can do it in 30 days and C alone can do it in 40 days in how many days will a alone do the work

Answer 1

A,B and C can do a piece of work together in 15 days.
B alone can do it in 30 days and C alone can do it in 40 days.
In how many days A alone will do the work?
:
Let a = no. of days required by A alone
let the completed job = 1
:
A typical shared work equation
:
15%2Fa + 15%2F30 + 15%2F40 = 1
Reduce the fractions
15%2Fa + 1%2F2 + 3%2F8 = 1
multiply by 8a, results
8(15) + 4a + 3a = 8a
120 + 7a = 8a
120 = 8a - 7a
a = 120 hrs A working alone
:
:
see if that adds up using a calc
15%2F120 + 15%2F30 + 15%2F40 =
.125 + .50 + .375 = 1; confirms our solution

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Answer 2

A B C can do work =15 days
for one day A B C will take 1/15 days
For one day B will take 1/30 days
For one day C will take 1/40 days
take the L.C.M of 15,30,40 is 720
1/15-1/30-1/40
(48-24-18)/720
(48-42)/720
6/720 so A alone will take 120 days