Question

8.) A and B together can do a piece of work in 12 days. B alone can finish it in 30 day
ow many days can A finish the same work?​

Answer 1

$\bf \: \underline{Given} \: :$ ↴

$\sf \: A \: and \: B \: together \: can \: do \: a \: piece \: of \: work \: in \: 12 \: days.$

$\sf \: B \: alone \: can \: finish \: it \: in \: 30 \: days.$

$\bf \: \underline{To \: find} :$ ↴

$\sf \: Number \: of \: days \: that \: A \: will \: take \: to \: finish \: the \: work.$

$\bf \: \star \: \underline{So, \: Let's \: Start } \: \star$

$\sf \: Time \: taken \: by \: A \: and \: B \: to \: finish \: the \: work = 12 \: days.$

$\sf \: Both \: (A \: and \: B)'s \: 1 \: day \: work \: = \: \pink{ \dfrac{1}{12} }$

$\sf \: Time \: taken \: by \: B \: to \: finish \: the \: work = 30 \: days.$

$\sf \: 1 \: day \: work = \pink{\dfrac{1}{30} }$

$\bf \: \underline{ Now},$

$\sf \: A's \: 1 \: day \: work :$ ↴

$\boxed{ \sf \:(A \: and \: B)'s \: 1 \: day \: work \: - \: \sf \: B's \: 1 \: day \: work.}$

$\sf \: \underline{Putting \: the \: values. }$

$\sf \: \longrightarrow \: \dfrac{1}{12} \: - \: \dfrac{1}{30}$

$\sf \: To \: subtract \: them \: we \: have \: to \: make \: the \: denominator \: same.$

$\sf \: \bigg(\dfrac{1}{12} \: \times \dfrac{5}{5} \: = \: \dfrac{5}{60} \bigg) \: - \bigg(\dfrac{1}{30} \: \times \dfrac{2}{2} \: = \: \dfrac{2}{60} \bigg)$

$\sf \: \longrightarrow \: \dfrac{5}{60} \: - \: \dfrac{2}{60}$

$\sf \: \longrightarrow \: \dfrac{5 - 2}{60}$

$\sf \: \longrightarrow \: \dfrac{3}{60} \: = \: \dfrac{1}{20}$

$\sf \: \underline{So, \: Answer \: = \: 20 \: days. }$

$\purple{\sf \: So, \: A \: will \: take \: 20 \: days \: to \: finish \: the \: same \: work.}$