Question

rajan can do piece of work In 24 days while while amit can do it in 30 days . in how many days can they complete it if they work together ​

Answer 1

Answer:

Add 24 and 30

24+30=54

ans: In 54 days rajan and amit can do 2 piece of work .

Answer 2

Number of days Rajan takes to do a piece of work =24 days.

Number of days Amit takes to do a piece of work = 30 days.

$\sf Work \:done \;in \;1 \;day \;by\; Rajan = \dfrac{1}{24}$

$\sf Work \:done \;in \;1 \;day \;by\; Amit = \dfrac{1}{30}$

Work done by Rajan and Amit  together in 1 day = Work done by Rajan 1 day + Work done by Amit in 1 day

$\sf Work \:done \:by \;Rajan\; and\; Amit\; together \:in \:1 \:day =\dfrac{1}{30} + \dfrac{1}{24}$

LCM of 30 and 24 = 120

$\implies\sf Work \;done\; by\; Rajan \;and \;Amit \; together\; in \;1 \;day = \dfrac{4+5}{120} = \dfrac{9}{120} = \dfrac{3}{40}$

$\sf They\; can\; complete \;the\; work \;together \;in\; \dfrac{40}{3} days.$