Question

Mukund and Nakul can paint their house in 10 days . Nakul and Rahul can paint the house in 15 days . Rahul and Mukund can paint the house in 20 days . In how many days can Mukund paint the house ?

Answer 1

I am denoting Mukund as = M
Nakul = N , and Rahul = R
now, M+N ==== 10 days
N+R ======= 15 days
R+M ======= 20 days
take the L.C.M of 10,15,20 = 60
means total work of painting is = 60 unit.
so 1 day work of M+N ==== 6 unit
1 day work of N+R ======= 4 unit
1 day work of R+M ======= 3 unit
if all person work together then their 1 day work will be ( M+N+N+R+R+M) = 6+4+3 = 13
2(M+N+R) = 13 so it will be
M+N+R = 13/2-------------------equation(1)
put the value of N+R = 4 in equation (1)
then M= (13/2)-4 = 5/2
if 1 day work of M is 5/2 unit= 2.5
then to complete 60 unit work he will take 60/2.5
= 600/25 = 24 days.