Delhi Police Constable Exam Model Paper 2

GIVEN:
A and C alone can do a piece of work in 12 days and 10 days respectively.
With the help of B, A can finish that work in 20/3 days
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 A, B and C alone to do the work
= ‘a’, ‘b’ and ‘c’ respectively.
Now,
$\frac{1}{12}+\frac{1}{\mathit{b}}=\frac{3}{20}$
⇒ b = 15 days
Now, required time:
$=\frac{1}{\left[\frac{1}{12}+\frac{1}{15}+\frac{1}{10}\right]}=\frac{60}{5+4+6}$
$=\frac{60}{15}$
= 4 days
Alternate Method
Let total work be 60 units. [LCM of 15, 10 and 15]
Now, efficiency of A = 60/12 = 5 units
Efficiency of C = 60/10 = 6 units
Efficiency of A + B = 60/(20/3/20) = 9 units
Now, efficiency of A + B + C = 9 + 6 = 15 units
∴ Required time = 60/15 = 4 days