In an annual function, 504 children participated. The ratio of the num

1.	In an annual function, 504 children participated. The ratio of the number of girls to the number of boys is 5 : 3 respectively. Out of the total girls, 20% participated in dance and remaining girls participated in solo song, group song and drama in the ratio of 2 : 3 : 4. Two – third of the total boys participated in group song and the remaining boys participated in solo song and dance in the ratio of 4:5What is the approximate percentage of the boys who have participated in dance out of the total number of boys?1). 19%2). 23%3). 16%4). 27%
Answer» Given that total number of students are 504 in which GIRLS to boys ratio is 5 : 3. Let the total number of girls be X then total number of boys will be (504 - X). $(\therefore \frac{X}{{504 - X}} = \frac{5}{3})$ 3X = 2520 – 5X ⇒ 8X = 2520 ⇒ Total number of girls, X = 315 And, total number of boys = 504 – 315 = 189 Now, given that 2/3^rd of boys participated in group song. Hence 1/3^rd of boys participated in solo song and dance in the ratio of 4:5. ⇒ One-third of total boys = 1/3 × 189 = 63 Let the number of boys participated in dance be D then, ∴ Number of boys participated in solo song = 63 – D Hence, $(\frac{{63 - D}}{D} = \frac{4}{5}\;)$ ⇒ 315 – 5D = 4D ⇒ 9D = 315 Hence, Number of boys participated in dance, D = 35 ∴ Required percentage = 35/189 × 100 = 18.518% ~ 19 %

In an annual function, 504 children participated. The ratio of the number of girls to the number of boys is 5 : 3 respectively. Out of the total girls, 20% participated in dance and remaining girls participated in solo song, group song and drama in the ratio of 2 : 3 : 4. Two – third of the total boys participated in group song and the remaining boys participated in solo song and dance in the ratio of 4:5What is the approximate percentage of the boys who have participated in dance out of the total number of boys?1). 19%2). 23%3). 16%4). 27%

Answer»

Given that total number of students are 504 in which GIRLS to boys ratio is 5 : 3.

Let the total number of girls be X then total number of boys will be (504 - X).

$(\therefore \frac{X}{{504 - X}} = \frac{5}{3})$

3X = 2520 – 5X

⇒ 8X = 2520

⇒ Total number of girls, X = 315

And, total number of boys = 504 – 315

= 189

Now, given that 2/3^rd of boys participated in group song.

Hence 1/3^rd of boys participated in solo song and dance in the ratio of 4:5.

⇒ One-third of total boys = 1/3 × 189

= 63

Let the number of boys participated in dance be D then,

∴ Number of boys participated in solo song = 63 – D

Hence, $(\frac{{63 - D}}{D} = \frac{4}{5}\;)$

⇒ 315 – 5D = 4D

⇒ 9D = 315

Hence, Number of boys participated in dance, D = 35

∴ Required percentage = 35/189 × 100

= 18.518%

~ 19 %