Let's solve the problem step-by-step.
Let the number of boys be \(B\) and the number of girls be \(G\).
According to the question, when 12 girls leave the group, the ratio of boys to girls becomes 2 : 1.
This can be expressed as:
\(\frac{B}{G - 12} = \frac{2}{1}\)
From this equation, we have:
\(B = 2(G - 12)\) ... (1)
Next, if 30 boys leave the group, the ratio of girls to boys becomes 3 : 1. This can be expressed as:
\(\frac{G - 12}{B - 30} = \frac{3}{1}\)
From this equation, we have:
\(G - 12 = 3(B - 30)\)
Expanding it, we get:
\(G - 12 = 3B - 90\)
Or, \(G = 3B - 78\) ... (2)
Now we have two equations:
- \(B = 2G - 24\) ... (from equation 1)
- \(G = 3B - 78\) ... (equation 2 from above)
Substituting the value of \(B\) from equation (2) into equation (1):
\(B = 2(3B - 78) - 24\)
This simplifies to:
\(B = 6B - 156 - 24\)
Simplification gives us:
\(5B = 180\)
\(B = 36\)
Substitute \(B = 36\) back into equation (2):
\(G = 3 \times 36 - 78\)
\(G = 108 - 78 = 30\)
Hence, the initial number of boys and girls are 36 and 30 respectively.
Correct Answer: 36 boys and 30 girls
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In a mixture of 156 litres, the ratio of milk and water is 7 : 6. How much water should be added to make the ratio 14 : 13?
If the ratio of the first to second number is 3 : 4 and that of the second to the third number is 8 : 5, and sum of three numbers is 190 then the third number is:
The third proportional to 9 and 15 is:
The average age of 3 persons is 30 years.If their ages are in the ratio of 3 : 5 : 7 respectively, then the age of the eldest person is:
The income of A and B are in the ratio 5 : 3. The expenses of A, B and C are in the ratio of 8 : 5 : 2. If C spends 2000 and B saves ₹ 700, then A saves:
