There were 100 boys in the park.The ratio of boys to girls was 2 : 3.After 20 boys left the park and some girls arrived at the park, the ratio of number of boysto the number of girls became 1 : 2.How many girls arrived at the park?
Question
There were 100 boys in the park.The ratio of boys to girls was 2 : 3.After 20 boys left the park and some girls arrived at the park, the ratio of number of boysto the number of girls became 1 : 2.How many girls arrived at the park?
Solution
Sure, let's solve this step by step:
Step 1: Initially, the ratio of boys to girls is 2:3. This means for every 2 boys, there are 3 girls. Since we know there were 100 boys, we can calculate the number of girls. If 2 parts represent 100 boys, then 1 part represents 50 (100/2) girls. Therefore, there were initially 150 (3*50) girls in the park.
Step 2: After 20 boys left the park, there were 80 (100-20) boys left.
Step 3: The problem states that after some girls arrived, the ratio of boys to girls became 1:2. This means for every 1 boy, there are 2 girls. So, if there are 80 boys, there should be 160 (80*2) girls to maintain this ratio.
Step 4: To find out how many girls arrived at the park, we subtract the initial number of girls from the final number of girls. So, 160 (final number of girls) - 150 (initial number of girls) = 10 girls.
Therefore, 10 girls arrived at the park.
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