Problem: Masud can do a job in 40 days working alone. Karim can do the same job :in 60 days working alone. They start working together and worked for 18 days, when Harun joined them. The three men worked together and finished the job in 5 days. In how many days could Harun do the whole job working alone?

Correct Answer: 120 days

Explanation:

Let the wholejob be 1 partMasud does in 40 days = 1 part

Masud does in 1 days =$\frac{1}{40}$’ part

Masud does in18 days =$\frac{18}{40}$ part

Similarly, Karim does in 60 days = 1 part

Karim does in 18 days = $\frac{18}{60}$ part

In 18 days they together did = $\frac{18}{60}$ + $\frac{18}{40}$ = $\frac{3}{4}$

Remain = (1 -$\frac{3}{4}$ ) part =$\frac{1}{4}$ part

$\frac{1}{4}$ part is done by the three in 5 days

In 5 days they did =$\frac{1}{4}$ part

In 1 day they did =’$\frac{1}{5}$ part

Now, In 1 day Masud & Karim together does = $\frac{1}{40}$+ $\frac{1}{60}$

In 1 day Harun dees = ($\frac{1}{20}$-$\frac{1}{24}$) = $\frac{1}{120}$ part

Harun alone does $\frac{1}{120}$ part in = 1 day

Harun alone does 1 part in 120 days.