Question

a do a piece of work in 3 days B and a together do the work in 2 days how many days will b be take to do the work

Answer 1

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Answer 2

$\texttt{Given : A do's the work in 3 Days}$

$\mathtt{\implies\;A\;do's\;\;\bigg(\dfrac{1}{3}\bigg)^{rd}\;of\;the\;work\;in\;one\;day}$

$\texttt{Given : A and B together do the work in 2 days}$

$\mathtt{\implies\;A\;and\;B\;together\;do\;\;\bigg(\dfrac{1}{2}\bigg)^{nd}\;of\;the\;work\;in\;one\;day}$

$\mathtt{\implies work\;done\;by\;A\;in\;one\;day + work\;done\;by\;B\;in\;one\;day = \dfrac{1}{2}}$

$\mathtt{\implies \dfrac{1}{3} + work\;done\;by\;B\;in\;one\;day = \dfrac{1}{2}}$

$\mathtt{\implies work\;done\;by\;B\;in\;one\;day = \bigg(\dfrac{1}{2} - \dfrac{1}{3}\bigg)}$

$\mathtt{\implies work\;done\;by\;B\;in\;one\;day = \bigg(\dfrac{3 - 2}{6}\bigg)}$

$\mathtt{\implies work\;done\;by\;B\;in\;one\;day = \bigg(\dfrac{1}{6}\bigg)}$

$\implies \texttt{B alone completes the work in 6 days}$