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The ratio of the number of students studying in schools A, B and C is 3:5:7 respectively. If the number of students studying in each of the schools is increased by 15%, 20% and 25% respectively, what will be the new respective ratio of the students in schools A, B and C?
- a)69:120:175
- b)120:69:175
- c)3:4:5
- d)13:14:15
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The ratio of the number of students studying in schools A, B and C is ...
Let the number of students in schools A, B and C be 3x, 5x and 7x respectively.
∴ Required ratio after respective increases
= (3 × 115) : (5 × 120) : (7 × 125 ) = 69 : 120 : 175
∴ Required ratio after respective increases
= (3 × 115) : (5 × 120) : (7 × 125 ) = 69 : 120 : 175
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The ratio of the number of students studying in schools A, B and C is ...
Given:
Ratio of students in schools A, B, and C = 3:5:7
Let's assume the initial number of students in schools A, B, and C to be 3x, 5x, and 7x respectively.
Increase in the number of students:
School A: 15% of 3x = (15/100)*3x = (9/20)x
School B: 20% of 5x = (20/100)*5x = x
School C: 25% of 7x = (25/100)*7x = (7/4)x
New number of students in schools A, B, and C:
School A: 3x + (9/20)x = (57/20)x
School B: 5x + x = 6x
School C: 7x + (7/4)x = (49/4)x
To find the new ratio of students, we need to simplify the above expression in terms of x and then find the ratio.
Calculating the new ratio:
Ratio of students in schools A, B, and C = [(57/20)x] : (6x) : [(49/4)x]
Dividing each term by x:
Ratio of students in schools A, B, and C = (57/20) : 6 : (49/4)
To compare the ratios, we need to make the denominators the same.
Multiplying the first ratio by 15/15, and the third ratio by 5/5:
Ratio of students in schools A, B, and C = (57/20)*(15/15) : 6 : (49/4)*(5/5)
Simplifying:
Ratio of students in schools A, B, and C = 855/300 : 6 : 245/20
Dividing each term by 5:
Ratio of students in schools A, B, and C = 171/60 : 6/5 : 49/4
Dividing each term by 3:
Ratio of students in schools A, B, and C = 57/20 : 2 : 49/12
Therefore, the new respective ratio of students in schools A, B, and C is 57:40:49, which can be simplified to 69:120:175. Hence, the correct answer is option A.
Ratio of students in schools A, B, and C = 3:5:7
Let's assume the initial number of students in schools A, B, and C to be 3x, 5x, and 7x respectively.
Increase in the number of students:
School A: 15% of 3x = (15/100)*3x = (9/20)x
School B: 20% of 5x = (20/100)*5x = x
School C: 25% of 7x = (25/100)*7x = (7/4)x
New number of students in schools A, B, and C:
School A: 3x + (9/20)x = (57/20)x
School B: 5x + x = 6x
School C: 7x + (7/4)x = (49/4)x
To find the new ratio of students, we need to simplify the above expression in terms of x and then find the ratio.
Calculating the new ratio:
Ratio of students in schools A, B, and C = [(57/20)x] : (6x) : [(49/4)x]
Dividing each term by x:
Ratio of students in schools A, B, and C = (57/20) : 6 : (49/4)
To compare the ratios, we need to make the denominators the same.
Multiplying the first ratio by 15/15, and the third ratio by 5/5:
Ratio of students in schools A, B, and C = (57/20)*(15/15) : 6 : (49/4)*(5/5)
Simplifying:
Ratio of students in schools A, B, and C = 855/300 : 6 : 245/20
Dividing each term by 5:
Ratio of students in schools A, B, and C = 171/60 : 6/5 : 49/4
Dividing each term by 3:
Ratio of students in schools A, B, and C = 57/20 : 2 : 49/12
Therefore, the new respective ratio of students in schools A, B, and C is 57:40:49, which can be simplified to 69:120:175. Hence, the correct answer is option A.
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The ratio of the number of students studying in schools A, B and C is 3:5:7 respectively. If the number of students studying in each of the schools is increased by 15%, 20% and 25% respectively, what will be the new respective ratio of the students in schools A, B and C?a)69:120:175b)120:69:175c)3:4:5d)13:14:15e)None of theseCorrect answer is option 'A'. Can you explain this answer?
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