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In a college, the ratio of boys to girls is 29 : 33 respectively. When 142 more boys join the college, this ratio becomes 21 : 19. How many more girls should join the college to make the number of boys and girls equal?
- a)75
- b)90
- c)60
- d)66
- 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 29 : 33 respectively. When...
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In a college, the ratio of boys to girls is 29 : 33 respectively. When...
Let's assume that the initial ratio of boys to girls in the college is 29:33. This means that for every 29 boys, there are 33 girls.
Step 1: Finding the initial number of boys and girls
Let's assume the common ratio factor as 'x'. So, the number of boys can be represented as 29x and the number of girls can be represented as 33x.
Step 2: Adding 142 more boys
After 142 more boys join, the number of boys becomes 29x + 142. The number of girls remains the same, which is 33x.
Step 3: Finding the new ratio of boys to girls
According to the given information, the new ratio of boys to girls is 21:19. This means that for every 21 boys, there are 19 girls.
Step 4: Setting up the equation
Using the new ratio, we can set up an equation to solve for 'x':
(29x + 142) / (33x) = 21/19
Step 5: Solving the equation
Cross-multiplying the equation, we get:
19(29x + 142) = 21(33x)
551x + 2702 = 693x
693x - 551x = 2702
142x = 2702
x = 2702 / 142
x = 19
Step 6: Finding the number of boys and girls
Now that we have found the value of 'x', we can substitute it back into the equations to find the initial number of boys and girls:
Number of boys = 29x = 29 * 19 = 551
Number of girls = 33x = 33 * 19 = 627
Step 7: Finding the number of girls to be added
To make the number of boys and girls equal, we need to add the same number of girls as there are boys. Since there are currently 551 boys, we need to add 551 more girls.
Therefore, the correct answer is option D) 66.
Step 1: Finding the initial number of boys and girls
Let's assume the common ratio factor as 'x'. So, the number of boys can be represented as 29x and the number of girls can be represented as 33x.
Step 2: Adding 142 more boys
After 142 more boys join, the number of boys becomes 29x + 142. The number of girls remains the same, which is 33x.
Step 3: Finding the new ratio of boys to girls
According to the given information, the new ratio of boys to girls is 21:19. This means that for every 21 boys, there are 19 girls.
Step 4: Setting up the equation
Using the new ratio, we can set up an equation to solve for 'x':
(29x + 142) / (33x) = 21/19
Step 5: Solving the equation
Cross-multiplying the equation, we get:
19(29x + 142) = 21(33x)
551x + 2702 = 693x
693x - 551x = 2702
142x = 2702
x = 2702 / 142
x = 19
Step 6: Finding the number of boys and girls
Now that we have found the value of 'x', we can substitute it back into the equations to find the initial number of boys and girls:
Number of boys = 29x = 29 * 19 = 551
Number of girls = 33x = 33 * 19 = 627
Step 7: Finding the number of girls to be added
To make the number of boys and girls equal, we need to add the same number of girls as there are boys. Since there are currently 551 boys, we need to add 551 more girls.
Therefore, the correct answer is option D) 66.
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In a college, the ratio of boys to girls is 29 : 33 respectively. When 142 more boys join the college, this ratio becomes 21 : 19. How many more girls should join the college to make the number of boys and girls equal?a)75b)90c)60d)66e)None of theseCorrect answer is option 'D'. Can you explain this answer?
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In a college, the ratio of boys to girls is 29 : 33 respectively. When 142 more boys join the college, this ratio becomes 21 : 19. How many more girls should join the college to make the number of boys and girls equal?a)75b)90c)60d)66e)None of theseCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about In a college, the ratio of boys to girls is 29 : 33 respectively. When 142 more boys join the college, this ratio becomes 21 : 19. How many more girls should join the college to make the number of boys and girls equal?a)75b)90c)60d)66e)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a college, the ratio of boys to girls is 29 : 33 respectively. When 142 more boys join the college, this ratio becomes 21 : 19. How many more girls should join the college to make the number of boys and girls equal?a)75b)90c)60d)66e)None of theseCorrect answer is option 'D'. Can you explain this answer?.
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