Time and Work Practice Test 3 with solutions

Here, A worked for 5 days, B for 7 days and C for 13 days = (A + B) worked for 5 days, (B + C) for 2 days and C for 11 days.
Let C will complete the work in x days,
Now, (A + B)'s 5 days' work + (B + C)'s 2 days' work + C's 11 days' work = $\frac{5}{12}+\frac{2}{16}+\frac{11}{\mathit{x}}$
= $\frac{13}{24}+\frac{11}{\mathit{x}}$
Again, $\frac{13}{24}+\frac{11}{\mathit{x}}$ = 1
⇒ $\frac{11}{\mathit{x}}$ = $\frac{11}{24}$
∴ x = 24
Hence, C would alone complete the work in 24 days.