Question

Solve for y. y/m + y/n = p

Answer 1

Given :

$\boxed{ \rm \frac{y}{m} + \frac{y}{n} = p}$

To find:

• Value of y

Step by step expansion:

$\dashrightarrow \sf\dfrac{y}{m} + \dfrac{y}{n} = p$

write the equation

$\dashrightarrow \sf \dfrac{\frac{y \times mn}{m} + \frac{y \times mn}{n}}{mn} = p$

Add y/n with y/n and we will get Lcm as mn

$\dashrightarrow \sf \dfrac{\frac{y \times \cancel mn}{\cancel m} + \frac{y \times m\cancel n}{\cancel n}}{mn} = p$

Cancel the similar terms

$\dashrightarrow \sf \dfrac{\frac{y \times n}{1} + \frac{y \times m}{1}}{mn} = p$

$\dashrightarrow \sf \dfrac{yn + ym}{mn} = p$

remove 1 as denominator

$\dashrightarrow \sf \dfrac{y(n + m)}{mn} = p$

take y as common

$\dashrightarrow \sf \dfrac{(n + m)}{mn} = \dfrac{p}{y}$

transfer y to other side as denominator of p

$\dashrightarrow \sf \dfrac{mn}{(n + m)} = \dfrac{y}{p}$

reciprocal the whole equation

$\dashrightarrow \sf \dfrac{mnp}{(n + m)} = \dfrac{y}{1}$

transfer p other side as numerator

$\dashrightarrow \boxed{ \bf y = \dfrac{mnp}{(n + m)} }$

$\therefore \red {\underline {\textbf{\textsf{Option 2 i.e \{y= mnp/(m+n) \} is correct }}}}$