Question

A and B can do a piece of work in 12 days B and C in 15 days and a and c in 20 days find the number of days in which all working together will complete the work . answer is 10 days​

Answer 1

solution: Let A, B & C do the work separately in a, b & c days separately.

Given, A and B can do a piece of work in 12 days

=> 1/a + 1/b = 1/12—————(1)

Given, B and C can do a piece of work in 15 days

=> 1/b + 1/c = 1/15—————(2)

Given, C and A can do a piece of work in 20 days

=> 1/c + 1/a = 1/20—————(3)

Adding all the three equations,

2(1/a + 1/b + 1/c) = 1/12 + 1/15 + 1/20

2(1/a + 1/b + 1/c) = (5+4+3)/60 = 12/60 = 1/5

=> 1/a + 1/b + 1/c = 1/10———(4)

(4) - (1)

=> (1/a + 1/b + 1/c) - (1/a + 1/b) = 1/10 - 1/12 = (6–5)/60 = 1/60

=> 1/c = 1/60

=> c = 60

=> C takes 60 days to do the work separately.

(4) - (2)

=>(1/a + 1/b + 1/c) - (1/b + 1/c) = 1/10 - 1/15 = (3–2)/30 = 1/30

=> 1/a = 1/30

=> a = 30

=> A takes 30 days to do the work separately.

(4) - (3)

=>(1/a + 1/b + 1/c) - (1/c + 1/a) = 1/10 - 1/20 = (2–1)/20 = 1/20

=> 1/b = 1/20

=> b = 20

=> B takes 20 days to do the work separately.