Question

2. A can do a job in 15 days, and B in 10 days. How many days will they take to finish the job
if they work together?
​

Answer 1

Answer:

30

Step-by-step explanation:

LCM of 15 and 10= 30 (process in the pic below.) Therefore, Ans--> The number of days A&B can do the work together is 30.

Answer 2

$\bf \underline{Given} :$

$\sf \implies A \: can \: do \: a \: job \: in \: 15 \: days.$

$\sf \implies B \: can \: do \: same \: job \: in \: 10 \: days.$

$\bf \underline{To \: find} :$

Total number of days which A and B will take if they will work together.

$\bf \underline{\underline{Solution } }$

$\sf \implies A's \: one \: day \: job = \dfrac{1}{15}$

$\sf \implies B's \: one \: day \: job = \dfrac{1}{10}$

$\sf \implies Work \: done\: by \:A \: and \: B \:together =\dfrac{1}{15} \: + \: \dfrac{1}{10}$

$\sf Take \: LCM \: to \: make \: the \: denominators \: same.$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\: \: 15 - 10\:\:\:}}}\\ {\underline{\sf{3}}}& \underline{\sf{\:\:15 - 5\:\:\:}} \\\underline{\sf{5}}&{\underline{\sf{\:\:5 - 5\:\:\:}}} \\ \underline{\sf{}}&{\sf{\:\:1\:\:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

$\sf LCM = 2 \times 3 \times 5 = 30$

$\sf \implies \dfrac{1 \times 2 = 2}{15 \times 2 = 30} \: + \: \dfrac{1 \times 3 = 3}{10 \times 3= 30}$

$\sf \implies \dfrac{2}{30} \: + \: \dfrac{3}{30}$

$\sf Take \: denominators \: as \: common.$

$\sf \implies \dfrac{2 + 3}{30} = \dfrac{5}{30}$

$\sf \implies \dfrac{5}{30} \: = \dfrac{1}{6}$

Hence, A and B together can complete the work in 6 days.