Given below are two quantities named I and II. Based on the given info

1.	Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers. The ratio of boys to girls in a school is 4 : 5. If 45 students from the same school left in the same ratio and 40 new girls joined the school, then the ratio of boys to girls becomes 4 : 9. Quantity I : What percentage of total students will be boys if 50% of the total number of boys leave the school? Quantity II : 30% 1. Quantity : I > Quantity : II2. Quantity : I ≥ Quantity : II3. Quantity : I
Answer» Correct Answer - Option 3 : Quantity : I < Quantity : II Let the number of boys = 4x and the number of girls = 5x If 45 students from the same school leave the school Then the number of boys left =\(\frac{45\times 4}{9}=20\) Then the number of girls left =\(\frac{45\times 5}{9}=25\) According to the question, \(\frac{{4x - 20}}{{5x - 25 + 40}} = \frac{4}{9} = > \frac{{4x - 20}}{{5x + 15}} = = \frac{4}{9}\) 36x – 180 = 20x + 60 16x = 240 x = 15 the number of boys = 4x = 4 × 15 = 60 and the number of girls = 5x = 5 × 15 = 75 When, 50% of the boys left then the remaining number of boys = 50% of 60 = 30 Total students = 30 + 75 = 105 \(Reqd. \% \frac{30\times 100}{105}=28.57%\)%

Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers. The ratio of boys to girls in a school is 4 : 5. If 45 students from the same school left in the same ratio and 40 new girls joined the school, then the ratio of boys to girls becomes 4 : 9. Quantity I : What percentage of total students will be boys if 50% of the total number of boys leave the school? Quantity II : 30% 1. Quantity : I > Quantity : II2. Quantity : I ≥ Quantity : II3. Quantity : I

Answer» Correct Answer - Option 3 : Quantity : I < Quantity : II

Let the number of boys = 4x and the number of girls = 5x

If 45 students from the same school leave the school

Then the number of boys left =\(\frac{45\times 4}{9}=20\)

Then the number of girls left =\(\frac{45\times 5}{9}=25\)

According to the question,
\(\frac{{4x - 20}}{{5x - 25 + 40}} = \frac{4}{9} = > \frac{{4x - 20}}{{5x + 15}} = = \frac{4}{9}\)

36x – 180 = 20x + 60

16x = 240

x = 15

the number of boys = 4x = 4 × 15 = 60

and the number of girls = 5x = 5 × 15 = 75

When, 50% of the boys left then the remaining number of boys = 50% of 60 = 30

Total students = 30 + 75 = 105

\(Reqd. \% \frac{30\times 100}{105}=28.57%\)%