Question

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 1

Answer:

Answer:

Given :-

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.

To Find :-

How many girls are at the banquet.

Solution :-

Let, the numbers of boys be 5x

And, the number of girls be 3x

But in halfway through the banquet 20 boys leave and the ratio becomes 5:4.

According to the question,

⇒ $\dfrac{5x - 20}{3x}$ = $\dfrac{5}{4}$

By doing cross multiplication we get,

⇒ 4(5x - 20) = 5(3x)

⇒ 20x - 80 = 15x

⇒ 20x - 15x = 80

⇒ 5x = 80

⇒ x = $\sf\dfrac{\cancel{80}}{\cancel{5}}$

➠ x = 16

Hence the required number of boys and girls are :

❐ Number of boys = 5x = 5(16) = 80

❐ Number of girls = 3x = 3(16) = 48

$\therefore$ 48 girls are at the banquet.

Answer 2

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 :-

⠀⠀⠀⠀

$\sf :\implies\: {\bold{\dfrac{5x - 20 }{3x } = \dfrac{5}{4}}}$

⠀⠀⠀⠀

$\sf :\implies\: {\bold{( 5x - 20)\times 4 = 5 \times 3x }}$

⠀⠀⠀⠀

$\sf :\implies\: {\bold{ 20x - 80 = 15x}}$

⠀⠀⠀⠀

$\sf :\implies\: {\bold{ 20x = 15 x + 80 }}$

⠀⠀⠀⠀

$\sf :\implies\: {\bold{ 20x - 15x = 80 }}$

⠀⠀⠀⠀

$\sf :\implies\: {\bold{ 5x = 80 }}$

⠀⠀⠀⠀

$\sf :\implies\: {\bold{ x = \dfrac{80}{5} }}$

⠀⠀⠀⠀

$\sf :\implies\: {\bold{ x = 16 }}$

⠀⠀⠀⠀

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