Question

In a village the total number of people is 250. If the number of men is 50 more than two-third of the number of women, find the number of men and women in the village​

Answer 1

$\red\star{\green{\boxed{\boxed{\boxed{\purple{\mathfrak{Answer:}}}}}}}\red\star$

Explanation:

$Let \:the\: number \:of \:women \:be \:x \:and\: no.\: of \:men\: be<strong><em> </em></strong>\:(\frac{2x}{3}+ 50).$

A/q:

$x+(\frac{2x}{3}+50)=250$

$x+\frac{2x}{3}+50=250$

$x+\frac{2x}{3}=250-50$

$\frac{3x+2x}{3}=200$

$\frac{5x}{3}=\frac{200\!\!\!\!/^\;100}{2\!\!\!\!/}$

$5x=100\times3$

$5x=300$

$x=\frac{300\!\!\!\!/^60}{5\!\!\!\!/}$

$x=60$

$Hence no. of women = 60$

$and\: no. \:of\: men = \frac{60\!\!\!\!/^20×2}{3\!\!\!\!/}+50 = (20×2)+50= 90$

Answer 2

$\Large\red\star{\green{\boxed{\boxed{\boxed{\purple{\rm{Answer:}}}}}}}\red\star$

$The \: no. \: of \: women \: is \: 120 \: \& \: the \: no. \: of \: men \: is \: 130$

$\Large\red\star{\green{\boxed{\boxed{\boxed{\purple{\mathfrak{Explanation:}}}}}}}\red\star$

$Let \:the\: number \:of \:women \:be \:x \\ \\</p><p>then, \: no.\: of \:men=<strong><em> </em></strong>\: \large\frac{2x}{3} \normalsize+ 50 = \large \frac{2x+150}{3}$

A/q:

$x+\Large \frac{2x+150}{3}$ $= 250$

$\implies \Large \frac{3x+2x+150}{3}$ $= 250$

$\implies \Large \frac{5x+150}{3}$ $= 250$

$\implies 5x+150= 750$

$\implies 5x =750-150$

$\implies 5x =600$

$\implies x = \Large\frac{600\!\!\!\!\!/}{5\!\!\!/}\;^{¹²⁰}$

$\implies x = 120$

$Hence, \: the \: no. \: of \: women = 120 \\</p><p>\& \: the \: no. \: of \: men = 250-120 = 130$