Subjects algebra

Region Girls Percentage 9559A5

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1. **Problem Statement:** We have 400 students in 2015 with 180 females. The region-wise breakup of students is given by angles: North = 126°, South = 144°, East and West = 90°. 2. **Calculate total students in each region:** The total angle in a pie chart is 360°. The number of students in each region is proportional to the angle. - North students = $\frac{126}{360} \times 400 = 140$ - South students = $\frac{144}{360} \times 400 = 160$ - East and West students = $\frac{90}{360} \times 400 = 100$ 3. **Calculate females in each region:** Total females = 180. Female distribution is proportional to the region angles. - Females in North = $\frac{126}{360} \times 180 = 63$ - Females in South = $\frac{144}{360} \times 180 = 72$ - Females in East and West = $\frac{90}{360} \times 180 = 45$ 4. **Calculate new girls joined in 2016:** Female population grew by 22.223%, so new girls = $180 \times \frac{22.223}{100} = 40$ 5. **Distribution of new girls by region:** - South new girls = 15% of 40 = $0.15 \times 40 = 6$ - East-West new girls = 25% of 40 = $0.25 \times 40 = 10$ - North new girls = remaining = $40 - 6 - 10 = 24$ 6. **Calculate total people in North region in 2016:** Original North students = 140, new girls in North = 24, so total North = $140 + 24 = 164$ 7. **Calculate percentage of new girls in North region:** $$\text{Percentage} = \frac{\text{New girls in North}}{\text{Total North students}} \times 100 = \frac{24}{164} \times 100 = 14.63\%$$ **Final answer:** 14.63% of the total people from the northern region in 2016 are the new girls who joined.