Question

A and B together can do a piece of work in 12 days while A alone can do the same work in 30 days. B alone can do it in

A) 18 days B) 20 days C) 15 days D) 22 days

Answer 1

Given :

• A and B together can do a piece of work in 12 days.
• A alone can do the same work in 30 days.

To find :

• B alone can do it in =?

Step-by-step explanation :

A and B together can do a piece of work in 12 days. [Given]

In 1 day they both can do the work together = 1/12 part.

A alone can do the same work in 30 days.[Given]

•°• A can do it in 1 day = 1/30 part.

Now,

B will do the work,

= 1/12 - 1/30

= 5-2/60

= 3/60

= 1/20

Therefore, B can do the work alone in 20 day's.

Hence, Option b) 20 days is the correct option.

Answer 2

Answer:

⠀⠀✩ (A + B) = 12 Days

⠀⠀✩ A = 30 Days

⠀$\rule{120}{0.8}$

☯ $\underline{\boldsymbol{According\: to \:the\: Question :}}$

$\dashrightarrow\sf\:\:(A+B)=\dfrac{A \times B}{A+B}\\\\\\\dashrightarrow\sf\:\:12 = \dfrac{30 \times B}{30 + B}\\\\\\\dashrightarrow\sf\:\:2 = \dfrac{5 \times B}{30 + B}\\\\\\\dashrightarrow\sf\:\:2(30 + B) = 5B\\\\\\\dashrightarrow\sf\:\:60 + 2B = 5B\\\\\\\dashrightarrow\sf\:\:60 = 5B - 2B\\\\\\\dashrightarrow\sf\:\:60 = 3B\\\\\\\dashrightarrow\sf\:\: \dfrac{60}{3} = B\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf B = 20\:Days}}$

⠀

$\therefore\:\underline{\textsf{Hence, B alone can do it in B) \textbf{20 Days}}}.$