Delhi Police Constable Exam Model Paper 7

Given:
A alone can complete a work = 10 days
A and B together complete the work in 6 days
Formula:
Total work = Efficiency × Time
Calculation:
Let total work be 30 (LCM of 10 and 6)
Efficiency of A = 3 units/day
Efficiency of (A + B) = 5 units/day
Efficiency of B = 5 – 3 = 2 units/day
Time taken by B to complete the work, x = 30/2 = 15 days
Alternate Solution
We know, Efficiency ∝ 1/Time
According to question,
$\frac{1}{10}+\frac{1}{\mathit{x}}=\frac{1}{6}$
⇒ $\frac{1}{\mathit{x}}=\frac{1}{6}-\frac{1}{10}$
⇒ $\frac{1}{\mathit{x}}=\frac{\left(5-3\right)}{30}$
⇒ $\frac{1}{\mathit{x}}=\frac{2}{30}=\frac{1}{15}$
⇒ $\mathit{x}=15$