Question : P and Q can complete a project in 15 days and 10 days, respectively. They started doing the work together, but after 2 days, Q had to leave and P alone completed the remaining work. In how many days was the whole work completed?
Option 1: 11
Option 2: 12
Option 3: 13
Option 4: 10
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Correct Answer: 12
Solution :
Given: P and Q can complete a project in 15 days and 10 days, respectively.
LCM of 15 and 10 is 30.
Let the work be 30 units.
Efficiency of P = $\frac{30}{15}=2$
Efficiency of Q = $\frac{30}{10}=3$
Two days of work of P and Q = 2 × (2 + 3) = 10 units
$\therefore$ Remaining work = 30 – 10 = 20 units
So, the number of days taken by P to complete 20 units of work $=\frac{20}{2}=10$
$\therefore$ Total days = 10 + 2 = 12 days
Hence, the correct answer is 12.
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