Question

. A and B together can complete a work in 10 days. A alone can complete the work in 15 days. If B does the work only half a day daily, then in how many days A and B together will complete the work
​

Answer 1

Given :

• A and B together can complete a work in 10 days.
• A alone can complete the work in 15 days.

To find :

• If B does the work only half a day daily, then in how many days A and B together will complete the work ?

Solution :

Let,

The one day work of B = $\sf \dfrac {1}{10} \ - \ \dfrac {1}{15}$

$\implies \sf \dfrac {3 \ - \ 2}{30}$

$\implies \sf \dfrac {1}{30}$

Together work of A and B in 1 day = $\sf \dfrac {1}{15} \ + \ \dfrac {1}{60}$

$\implies \sf \dfrac {4 \ + \ 1}{60}$

$\implies \sf \dfrac {\cancel{5}}{\cancel{60}}$

$\implies \sf \dfrac {1}{12}$

Therefore, B works half day only.

$\therefore$ A and B together will complete the work in 12 days.

Answer 2

Questions :-

→ A and B together can complete a work in 10 days. A alone can complete the work in 15 days. If B does the work only half a day daily, then in how many days A and B together will complete the work

​

Given :-

→ A and B together can complete a work in 10 days

→ A alone can complete the work in 15 days

To Find :-

→  If B does the work only half a day daily, then in how many days A and B together will complete the work ?

Solution :-

$\sf A\;and\;B\;complete\;a\;work\;in\;=\;10\;days\\\\\\One\;day's \;work\;of \; (A + B) \; = \dfrac{1}{10} \\\\\\A\;alone\;can\;complete\;the\;work\;in\; = 15 \; days \\\\One\;day's\;work\;of\;A\;= \dfrac{1}{15} \; days \\\\\\Then\;B's\;one\;day\;work\;=\; \dfrac{1}{10} - \dfrac{1}{15} \\\\\longrightarrow \dfrac{3-2}{30} \\\\\\\longrightarrow \dfrac{1}{30} \;days$

∴ B alone can complete the work in = 30 days.

$\sf Together\;work\;of\;A\;and\;B\;in\;1\;day\; = \dfrac{1}{15} + ( \dfrac{1}{30} \times \dfrac{1}{2} )\\\\\\\longrightarrow \dfrac{1}{15} + \dfrac{1}{60} \\\\\\\longrightarrow \dfrac{1}{12} [B\;works\;for\;half\;day\;only]\\\\\\So,\;A\;and\;B\;together\;will\;complete\;the\;work\;in\;12\;days.$