Directions: Study the information carefully to answer the question that follows 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 s

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Directions: Study the information carefully to answer the question that follows 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 s

Asked on 2019-05-18 10:09:43 by Guest | Votes 24 | Views: 179 | Tags: miscellaneous | mix | Add Bounty

Directions: Study the information carefully to answer the question that follows

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 4:5
What 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%

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29 vote

Answered by Guest on 2019-05-28 17:15:56 | Votes 29 | #

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 %

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