two thousand people live in business village of which 55% were male. the male population earned 5 % and female population earned 8% on an investment of rs. 50 each. find the change in the % profit of the village if the ratio of male to female gets reversed the next year and population remain same
To find the change in the percentage profit of the village, we need to determine the profit earned by each gender in both scenarios and then calculate the percentage change.
Let's break down the problem step by step:
Step 1: Calculate the number of males and females in the village:
Total population = 2000
Males = 55% of 2000 = 0.55 * 2000 = 1100
Females = Total population - Males = 2000 - 1100 = 900
Step 2: Calculate the profit earned by each gender:
Investment per person = Rs. 50
Profit earned by males = 5% of Rs. 50 = 0.05 * 50 = Rs. 2.50
Profit earned by females = 8% of Rs. 50 = 0.08 * 50 = Rs. 4.00
Step 3: Calculate the total profit earned by the village:
Total profit = (Profit earned by males * Number of males) + (Profit earned by females * Number of females)
Total profit = (2.50 * 1100) + (4.00 * 900) = Rs. 2750 + Rs. 3600 = Rs. 6350
Step 4: Calculate the percentage profit of the village in the initial scenario:
Percentage profit = (Total profit / Total investment) * 100
Total investment = Total population * Investment per person = 2000 * 50 = Rs. 100000
Percentage profit = (6350 / 100000) * 100 = 6.35%
Step 5: Determine the new ratio of males to females in the next year:
The ratio of males to females gets reversed, meaning the number of males and females switches.
New males = 900
New females = 1100
Step 6: Calculate the profit earned by each gender in the reversed scenario:
Profit earned by new males = 8% of Rs. 50 = 0.08 * 50 = Rs. 4.00
Profit earned by new females = 5% of Rs. 50 = 0.05 * 50 = Rs. 2.50
Step 7: Calculate the total profit earned by the village in the reversed scenario:
Total profit in the reversed scenario = (Profit earned by new males * Number of new males) + (Profit earned by new females * Number of new females)
Total profit in the reversed scenario = (4.00 * 900) + (2.50 * 1100) = Rs. 3600 + Rs. 2750 = Rs. 6350
Step 8: Calculate the percentage profit of the village in the reversed scenario:
Percentage profit in the reversed scenario = (Total profit in the reversed scenario / Total investment) * 100
Percentage profit in the reversed scenario = (6350 / 100000) * 100 = 6.35%
Step 9: Calculate the change in the percentage profit:
Change in percentage profit = Percentage profit in the reversed scenario - Percentage profit in the initial scenario
Change in percentage profit = 6.35% - 6.35% = 0%
Therefore, there is no change in the percentage profit of the village if the ratio of males to females gets reversed while the population remains the same.