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In a school having roll strength 299, the ratio of boys and girls is 8 : 5. If 25 more girls get admitted into the school, the ratio of boys and girls becomes
- a)46: 35
- b)43: 35
- c)56: 33
- d)53: 33
Correct answer is option 'A'. Can you explain this answer?
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In a school having roll strength 299, the ratio of boys and girls is 8...
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In a school having roll strength 299, the ratio of boys and girls is 8...
To solve this problem, let's break it down step by step:
Given information:
- Total roll strength of the school = 299
- Ratio of boys to girls = 8:5
Step 1: Finding the number of boys and girls in the school
Let's assume the number of boys is 8x and the number of girls is 5x, where x is a common factor.
According to the given information, the total roll strength is 299. So, we can write the equation:
8x + 5x = 299
Combining like terms, we get:
13x = 299
Solving for x, we find:
x = 299/13
x ≈ 23
So, the number of boys = 8x ≈ 8 * 23 = 184
And the number of girls = 5x ≈ 5 * 23 = 115
Step 2: Adding more girls to the school
Now, let's consider that 25 more girls are admitted to the school. So, the new number of girls will be 115 + 25 = 140.
Step 3: Finding the new ratio of boys to girls
The new ratio of boys to girls can be calculated as:
184 : 140
To simplify the ratio, we can divide both numbers by their greatest common divisor (GCD), which is 4 in this case:
184 ÷ 4 : 140 ÷ 4
46 : 35
So, the new ratio of boys to girls is 46:35.
Therefore, the correct answer is option A) 46:35.
Given information:
- Total roll strength of the school = 299
- Ratio of boys to girls = 8:5
Step 1: Finding the number of boys and girls in the school
Let's assume the number of boys is 8x and the number of girls is 5x, where x is a common factor.
According to the given information, the total roll strength is 299. So, we can write the equation:
8x + 5x = 299
Combining like terms, we get:
13x = 299
Solving for x, we find:
x = 299/13
x ≈ 23
So, the number of boys = 8x ≈ 8 * 23 = 184
And the number of girls = 5x ≈ 5 * 23 = 115
Step 2: Adding more girls to the school
Now, let's consider that 25 more girls are admitted to the school. So, the new number of girls will be 115 + 25 = 140.
Step 3: Finding the new ratio of boys to girls
The new ratio of boys to girls can be calculated as:
184 : 140
To simplify the ratio, we can divide both numbers by their greatest common divisor (GCD), which is 4 in this case:
184 ÷ 4 : 140 ÷ 4
46 : 35
So, the new ratio of boys to girls is 46:35.
Therefore, the correct answer is option A) 46:35.
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