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In a college, the ratio of boys to girls is 31: 23 respectively. When 75 more girls join the college, this ratio becomes 124: 107. How many more girls should join the college to make the number of boys and girls equal?
- a)75
- b)90
- c)60
- d)85
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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In a college, the ratio of boys to girls is 31: 23 respectively. When ...
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In a college, the ratio of boys to girls is 31: 23 respectively. When ...
Given:
Ratio of Boys to Girls in the college = 31:23
Ratio of Boys to Girls in the college after 75 girls join = 124:107
To find:
How many more girls should join the college to make the number of boys and girls equal?
Solution:
Let the number of boys and girls in the college be 31x and 23x respectively.
After 75 girls join the college, the number of girls becomes 23x + 75, and the ratio of boys to girls becomes 124:107.
So, we can write:
31x / (23x + 75) = 124/107
Solving this equation, we get:
x = 255
So, the current number of boys and girls in the college are:
Boys = 31x = 31 × 255 = 7905
Girls = 23x = 23 × 255 = 5865
To make the number of boys and girls equal, we need to add (7905 - 5865) = 2040 more girls.
But we already have 75 more girls than before, so we need to add only (2040 - 75) = 1965 more girls.
Therefore, the answer is option (d) 85.
Ratio of Boys to Girls in the college = 31:23
Ratio of Boys to Girls in the college after 75 girls join = 124:107
To find:
How many more girls should join the college to make the number of boys and girls equal?
Solution:
Let the number of boys and girls in the college be 31x and 23x respectively.
After 75 girls join the college, the number of girls becomes 23x + 75, and the ratio of boys to girls becomes 124:107.
So, we can write:
31x / (23x + 75) = 124/107
Solving this equation, we get:
x = 255
So, the current number of boys and girls in the college are:
Boys = 31x = 31 × 255 = 7905
Girls = 23x = 23 × 255 = 5865
To make the number of boys and girls equal, we need to add (7905 - 5865) = 2040 more girls.
But we already have 75 more girls than before, so we need to add only (2040 - 75) = 1965 more girls.
Therefore, the answer is option (d) 85.
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