Question

P and Q can do a piece of work in 20days. after 12 they worked P left the work. Q did the remaining work in 10days. in how many days can P do separately and Q do separately?​

Answer 1

        $\text{\huge \bf \underline{Answer:}}$

        $\text{Work done by P and Q in 20 days} = 1$

        $\text{Work done by P and Q in 1 day} = \dfrac{1}{20}$

        $\text{Work done by P and Q in 12 days} = \dfrac{1}{20} \times 12 = \dfrac35$

$\implies \: \text{Work remaining after P and Q worked for 12 days} = 1 - \dfrac35 = \dfrac25$

        $\text{Time taken by Q to finish }\dfrac25 \text{ of the work} = 10 \text{ days}$

$\implies \: \boxed{\boxed{\text{Time taken by Q to finish the complete work} = 10 \times \dfrac52 = 25 \text{ days}}}$

$\implies \: \text{Work done by Q in 25 days} = 1$

$\implies \: \text{Work done by Q in 1 day} = \dfrac{1}{25}$

        $\text{Let the work done by P in 1 day be }\dfrac{1}{x}$

$\implies \: \text{Work done together by P and Q in 1 day} = \dfrac{1}{25} + \dfrac{1}{x} = \dfrac{1}{20}$

$\implies \: \dfrac{1}{x} = \dfrac{1}{20} - \dfrac{1}{25}$

$\implies \: \dfrac{1}{x} = \dfrac{5 - 4}{100}$

$\implies \: \dfrac{1}{x} = \dfrac{1}{100}$

$\implies \: \text{Work done by P in 1 day} = \dfrac{1}{100}$

$\implies \: \boxed{\boxed{\text{Time taken by P to complete the work} = 100 \text{ days}}}$