Question

A does a work in 10 day and b in 15 day i how many days they together will do the same work

Answer 1

$\bold{\boxed{Solution:}}$

A can do a work in 10 days.

A's one day's work = $\frac{1}{10}$

B can do a work in 15 days.

B's one day's work = $\frac{1}{15}$

Now,

Both can do a same work together in

$\frac{1}{10} + \frac{1}{15} \\ \\ \frac{3+ 2}{30} \\ \\ \frac{ 5}{30} = \frac{1}{6}$

$\bold{Both \:can\: do\: work \:in\: 6\: days}$

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$\textbf{Thank you!!}$

Answer 2

$\textbf{Solution:}$
________


$\bf{A}$ can do a work in $\bf{\underline{10\:days}}$

So, one day's work done by $\bf{A}$ = $\bold{\large{ \frac{1}{10} }}$

$\bf{B}$ can do a work in $\bf{\underline{15\:days}}$

One day's work done by $\bf{B}$ = $\bold{\large{ \frac{1}{15} }}$

Now,

= > $\bold{\large{ \frac{1}{10} + \frac{1}{15} }}$

$\bold{( L.C.M \: of \: 10 \: and \: 15 \: is \: 30)}$

= > $\bold{\large{ \frac{ 3 + 2}{30} }}$

= > $\bold{\large{ \frac{5}{30} = \frac{1}{6} }}$

= > $\bold{\boxed{\large {= 6}}}$

$\textbf{\underline{Thus, both can do work in 6 days}}$

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$\textbf{Hope It Helps !!!}$