Question

S and T can do a piece of work in 40 days and 24 days respectively. S started the work alone and then after 5 days T joined him till the completion of the work. How long did the work last?

• A. 12.5 days
• B. 18.675 days
• C. 13.125 days
• D. 20 days
• E. 18.125 days

Answer 1

The correct option is E

18.125 days

Work done by S in 5 days = $(\frac{1}{40}\times 5)=\frac{1}{8}$,
Remaining work = $(1-\frac{1}{8})=\frac{7}{8}$

(S + T)'s 1 day's work = $(\frac{1}{40}+\frac{1}{24})=\frac{8}{120}=\frac{1}{15}$

Now, $\frac{1}{15}$ work is done by S and T in $1day$.

So, $\frac{7}{8}$ work will be done by S and T in $(15\times \frac{7}{8})$ \\ = $13.125days$

Hence, total time taken = $(13.125+5)days=18.125days$