At a banquet the ratio of the number of boys to the number of girls is

1.	At a banquet the ratio of the number of boys to the number of girls is 5:3. Halfway through the banquet 20 boys leave and the ratio becomes 5:4. How many girls are at the banquet?
Answer» $\sf{\bold{\green{\underline{\underline{Given}}}}}$ ⠀⠀⠀⠀ Ratio of boys : girls = 5 : 3 Ratio after 20 boys left = 5 : 4 ⠀⠀⠀⠀ ______________________ $\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$ ⠀⠀⠀⠀ No. of girls = ?? ______________________ $\sf{\bold{\green{\underline{\underline{Solution}}}}}$ ⠀⠀⠀⠀ let the no. of boys and the no. of girls be 5x and 3x ⠀⠀⠀⠀ Acc. to the question :- ⠀⠀⠀⠀ $\sf :\implies\: {\bold{\dfrac{<klux>5X</klux> - 20 }{3x } = \dfrac{5}{4}}}$ ⠀⠀⠀⠀ $\sf :\implies\: {\bold{( 5x - 20)\times 4 = 5 \times 3x }}$ ⠀⠀⠀⠀ $\sf :\implies\: {\bold{ 20x - 80 = 15x}}$ ⠀⠀⠀⠀ $\sf :\implies\: {\bold{ 20x = 15 x + 80 }}$ ⠀⠀⠀⠀ $\sf :\implies\: {\bold{ 20x - 15x = 80 }}$ ⠀⠀⠀⠀ $\sf :\implies\: {\bold{ 5x = 80 }}$ ⠀⠀⠀⠀ $\sf :\implies\: {\bold{ x = \dfrac{80}{5} }}$ ⠀⠀⠀⠀ $\sf :\implies\: {\bold{ x = <klux>16</klux> }}$ ⠀⠀⠀⠀ Putting value of x in the no. of girls ⠀⠀⠀⠀ No. of girls = 3x ⠀⠀⠀⠀ No. of girls = 3 × 16 ⠀⠀⠀⠀ No. of girls = 48 ______________________ $\sf{\bold{\green{\underline{\underline{Answer}}}}}$ ⠀⠀ Number of girls in the banquet is 48