Problem Setup: Ratio of Girls to Boys
Let G8 and B8 be the number of girls and boys in Class VIII.
Let G9 and B9 be the number of girls and boys in Class IX.
We are given:
- Total students in Class VIII: $G8 + B8 = 450$
- Total students in Class IX: $B9 + G9 = 360$
- The ratio of girls to boys in Class VIII is the same as the ratio of boys to girls in Class IX: $\frac{G8}{B8} = \frac{B9}{G9}$
- The number of girls in both classes is the same: $G8 = G9$
We need to find the value of $G8$ (or $G9$). Let $G = G8 = G9$.
Calculating Student Numbers
From the total students, we can express the number of boys in terms of $G$:
- For Class VIII: $B8 = 450 - G8 = 450 - G$
- For Class IX: $B9 = 360 - G9 = 360 - G$
Solving the Ratio Equation
Substitute these expressions into the ratio equation $\frac{G8}{B8} = \frac{B9}{G9}$:
$ \frac{G}{450 - G} = \frac{360 - G}{G} $
Cross-multiply:
$ G \times G = (450 - G) \times (360 - G) $
$ G^2 = 450 \times 360 - 450G - 360G + G^2 $
$ G^2 = 162000 - 810G + G^2 $
Subtract $G^2$ from both sides:
$ 0 = 162000 - 810G $
Rearrange to solve for $G$:
$ 810G = 162000 $
$ G = \frac{162000}{810} $
$ G = \frac{16200}{81} $
$ G = 200 $
Conclusion
The number of girls in each class ($G8$ and $G9$) is 200.
Important Questions from Ratio and Proportion
The cost of a diamond is directly proportional to the square of its weight. The cost of a 14 gm diamond is Rs. 2560. This diamond got broken down into two pieces in the ratio of 5 ∶ 9. How much loss percent is incurred due to this breakage ? (Correct to two decimal places)
Atul purchased Bread costing Rs.20 and gave a 100 rupee note to the shopkeeper. The shopkeeper gave the balance money in coins of denomination Rs.2, Rs.5 and Rs.10. If these coins are in the ratio 5 ∶ 4 ∶ 1, then how many Rs.5 coins did the shopkeeper give?
A person divides a certain amount among his three sons in the ratio of 3 ∶ 4 ∶ 5. If he had divided this amount in the ratio of 1/3,1/4,1/5, his son, who had got the lowest share earlier, would get Rs.1,188 more. Find the amount (in Rs).
In a school 3/8 of the number of students are girls and the rest are boys. One-third of the number of boys are below 10 years and 2/3 the number if girls are also below 10 years. If the number of students of age 10 or more years is 260. then the number of boys in the school is:
If a : b : c = \(\frac{1}{4} : \frac{1}{3} : \frac{1}{2}, \) then \( \ \frac{a}{b} : \frac{b}{c} : \frac{c}{a} = ?\)
