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What is the number of girls if the total number of students is 2400 and the ratio of boys to girls is 7:5?
  • a)
    2500
  • b)
    1000
  • c)
    1500
  • d)
    1550
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
What is the number of girls if the total number of students is 2400 an...
Given:
Total students = 2400
Ratio of boys to girls = 7: 5
Concept used:
Total ratio units = sum of the ratio parts
Number of girls = (total students × girl's ratio units) / total ratio units
Calculation:
Total ratio units = 7 + 5 = 12
⇒ Number of girls = (2400 × 5) / 12
⇒ Number of girls = 12000 / 12
⇒ Number of girls = 1000
∴ The number of girls is 1000.
Alternate Method
Concept used:
Use the concept of proportional ratios.
Calculation:
Set up the ratio equation for girls (G) based on the given ratio:
Boys (B) : Girls (G) = 7 : 5
Express the ratio in terms of a variable (let x be the common multiplier):
B = 7x & G = 5x
Sum of the ratios equals the total number of students:
7x + 5x = 2400
Combine like terms:
12x = 2400
⇒ x = 200
Find the number of girls (G):
G = 5 × 200
⇒ G = 1000
∴ The number of girls is 1000.
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