Find Total Work using LCM

Assume the total work is the LCM of the individual completion days, which is the LCM of 10 and 15.

$\text{LCM}(10, 15) = 30 \text{ units}$

Calculate Daily Work Rates

Determine the amount of work completed by P and Q in one day.

$P_{\text{1-day}} = \frac{30}{10} = 3, \quad Q_{\text{1-day}} = \frac{30}{15} = 2$

Calculate Work Done Together in 3 Days

Multiply the combined daily rate by the 3 days they worked together.

$\text{Work done} = (3 + 2) \times 3 = 15 \text{ units}$

Calculate Remaining Work and Time for Q

Subtract the completed work from the total work, then divide by Q's daily rate.

$Q_{\text{days}} = \frac{30 - 15}{2} = \frac{15}{2} = 7.5 \text{ days}$