Question

2 men and 3 boys can do a piece of work in 20 days. While 3 men and 4 days can do it in 14 days. How long would it take one boy to finish the work?(WITH WORKING) ASAP​

Answer 1

$\texttt{2 Men and 3 Boys can do the work in 20 days}$

$\implies \mathtt{Work\;done\;by\;2\;Men\;and\;3\;Boys\;in\;one\;day = \dfrac{1}{20}}$

$\mathtt{\implies 2M + 3B = \dfrac{1}{20}}$

$\texttt{Multiplying above equation with 3}$

$\mathtt{\implies 6M + 9B = \dfrac{3}{20}\;----(1)}$

$\texttt{3 Men and 4 Boys can do the work in 14 days}$

$\implies \mathtt{Work\;done\;by\;3\;Men\;and\;4\;Boys\;in\;one\;day = \dfrac{1}{14}}$

$\mathtt{\implies 3M + 4B = \dfrac{1}{14}}$

$\texttt{Multiplying above equation with 2}$

$\mathtt{\implies 6M + 8B = \dfrac{2}{14}\;----(2)}$

$\texttt{Subtracting Equation (2) from Equation (1)}$

$\mathtt{\implies 6M + 9B - (6M + 8B) = \dfrac{3}{20} - \dfrac{2}{14}}$

$\mathtt{\implies 6M + 9B - 6M - 8B = \dfrac{3}{20} - \dfrac{1}{7}}$

$\mathtt{\implies B = \dfrac{7(3) - 20}{140}}$

$\mathtt{\implies B = \dfrac{21 - 20}{140}}$

$\mathtt{\implies B = \dfrac{1}{140}}$

$\implies \mathtt{Work\;done\;by\;One\;Boy\;in\;one\;day = \dfrac{1}{140}}$

$\implies \texttt{One Boy completes the work in 140 Days}$