Delhi Police Constable Exam Model Paper 10

GIVEN: P and Q together can finish the work in 18.75 days
Q and R together can finish that work in 50/3 days
All the three persons together can finish that work in 75/7 days
CONCEPT:
Time and Work
FORMULA USED:
Time taken by A and B together to finish the work:
$\frac{1}{\left[\frac{1}{\mathit{A}}+\frac{1}{\mathit{B}}\right]}$
CALCULATION:
Let time taken by P, Q and R alone to do the work = ‘p’, ‘q’ and ‘r’ respectively.
Now,
$\frac{1}{\mathit{p}}+\frac{1}{\mathit{q}}=\frac{1}{18.75}=\frac{4}{75}------\left(1\right)$
$\frac{1}{\mathit{q}}+\frac{1}{\mathit{r}}+\frac{1}{\mathit{r}}=\frac{3}{50}----\left(2\right)$
$\frac{1}{\mathit{q}}+\frac{1}{\mathit{q}}+\frac{1}{\mathit{r}}=\frac{7}{75}$ -- (3)
From (1) and (3):
$\frac{4}{75}+\frac{1}{\mathit{r}}=\frac{7}{75}$
⇒ r = 25
From (2) and /(3):
$\frac{1}{\mathit{q}}+\frac{3}{50}=\frac{7}{75}$
⇒ p = 30
Now, required time:
$=\frac{1}{\left[\frac{1}{30}+\frac{1}{25}\right]=}\frac{150}{5+6}=\frac{150}{11}$ days