Concept of "CASELET-2"

Directions (Q. No. 1-5): 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 the remaining girls participated in solo song, group song and drama in the ratio of 2: 3: 4. Two-thirds of the total boys participated in group song and the remaining boys participated in solo song and dance in the ratio of 4: 5

Q. 1. What is the approximate percentage of the boys who have participated in dance out of the total number of boys? [Ans. (1) 19%]

(1) 19%   (2) 23%   (3) 16%   (4) 27%   (5) 14%

Q. 2. What is the approximate percentage of the girls who participated in solo song out of the total participants? [Ans. (1) 11%]

(1) 11%   (2) 15%   (3) 6%   (4) 20%   (5) 18%

Q. 3. What is the total number of girls who have participated in group song and drama together? [Ans. (2) 196]

(1) 192   (2) 196   (3) 184   (4) 168   (5) 175

Q. 4. What is the ratio of the number of boys to the number of girls who have participated in solo dance? [Ans. (1) 1: 2]

(1) 1: 2   (2) 2: 1   (3) 4: 3   (4) 3: 2   (5) None of these

Q. 5. What is the difference between the number of boys and that of girls who have participated in dance? [Ans. (3) 28]

(1) 63   (2) 35   (3) 28   (4) 126   (5) None of these

Solution:

Detailed Explanation: Total no. of children = 504

The ratio of the number of girls to the number of boys is 5: 3 respectively.

So, 8 ≡ 504

Or, 1≡? = 63

The number of girls = 5 ≡ 63×5 = 315

The number of boys = 3 ≡ 63×3 = 189

The number of girls participated in dance = 20% of 315 = 63

Remaining girls = 315-63 = 252

Remaining girls (252) participated in solo song, group song and drama in the ratio of 2: 3: 4.

9 ≡ 252

Or, 1≡? = 28

The number of girls participated in solo songs = 2 ≡ 28×2 = 56

The number of girls participated in group songs = 3 ≡ 28×3 = 84

The number of girls participated in drama = 4 ≡ 28×4 = 112

The number of boys participated in group songs = 2/3^rd of 189 = 126

Remaining number of boys = 189-126 = 63

Remaining boys (63) participated in solo songs and dance in the ratio of 4: 5

So, 9 ≡ 63

Or, 1≡? = 7

The number of boys participated in solo songs = 4 ≡ 7×4 = 28

The number of boys participated in dance = 5 ≡ 7×5 = 35

Q. 1. 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%   (5) 14%

Sol. The question is: 35 is what percent of 189 (approximately)?

Here, So, 189 ≡ 100%

         Or, 18.9 ≡10% ≡ 19 (approx) or, 38 ≡ 20%

         Or, 1.89 ≡1% ≡ 1.9 (approx) or, 3.8 ≡ 2.0%

35 is approximately 20%-2% = 18% (above 18%)

So, 19% approximately. Ans.

Q. 2. What is the approximate percentage of the girls who participated in solo song out of the total participants?

(1) 11%   (2) 15%   (3) 6%   (4) 20%   (5) 18%

Sol. The question is: 56 is what percent of 504 (approximately)?

Here, So, 504 ≡ 100%

         Or, 50.4 ≡10%

         Or, 5.04 ≡1%

56 is approximately 10%+1% = 11% Ans.

Q. 3. What is the total number of girls who have participated in group song and drama together?

(1) 192   (2) 196   (3) 184   (4) 168   (5) 175

Sol. The total number of girls who have participated in group song and drama together = 84+112 = 196 Ans.

Q. 4. What is the ratio of the number of boys to the number of girls who have participated in solo song?

(1) 1: 2   (2) 2: 1   (3) 4: 3   (4) 3: 2   (5) None of these

Sol. The ratio of the number of boys to the number of girls who have participated in solo song = 28: 56 = 1: 2 Ans.

Q. 5. What is the difference between the number of boys and that of girls who have participated in dance?

(1) 63   (2) 35   (3) 28   (4) 126   (5) None of these

Sol. The difference between the number of boys and that of girls who have participated in dance = 63-35 = 28 Ans.