Question

Working together,Prathap and Do keep can paint their apartment in 2 days.Working alone,Prathap can complete the job in 3days less than Do keep.How long would it take each person working alone?

Answer 1

Solution-: We have this situation

completion time, in days

Do= T

Prathap =T – 3

together= 2 days

Inverting, I can tabulate their per-day completion rates:

completed per day:

Do=1/T ​​

Prathap = 1/(T-3)

​​

together= 1/2
According to condtion we get
1/T + 1/ (T-3)​ = 1/2
or (T-3 +T)/(T)*(T-3)=1/2

or (2T-3)/(T^2-3T)=1/2
By cross multiply
2(2T-3)= T^2-3T
4T-6 =T^2-3T
T^2-3T-4T+6=0

T^2-7T+6=0 we will factorize now
( T-6)(T-1)=0
T-6=0 or T-1=0
T=6 and T = 1
If we take T=1 it will give negative days if we plug in T-3 = 1-3 =-2 Since days never be in negative
So we will neglect T=1 , So we will take T = 6 days

So do work alone in 6 days
And Prathap = T-3 = 6-3 = 3 days
So answer is 6 and 3 days .​