Question

The ratio of the number of boys in schools A and of B is 5 ∶ 7 and the ratio of the total number of students in A and B is 3 ∶ 4. If the number of girls in B is equal to 66$\frac{2}{3}$ % of the total students in B, then what is the ratio of the number of girls in A and B?

• A. 43 ∶ 46
• B. 8 ∶ 11
• C. 43 ∶ 56
• D. 33 ∶ 56

Answer 1

Answer:

A. 43 ∶ 46

Given:

The ratio of the number of boys in schools A and of B is 5 ∶ 7 and the ratio of the total number of students in A and B is 3 ∶ 4.

The number of girls in B is equal to 662323% of the total students in B.

Calculation:

	Section A	Section B
Boys	5x	7x
Total Students	3y	4y

Number of girls in B = Total students - Boys

Number of girls in B = (4y - 7x)

Similarly,

Number of girls in A = (3y - 5x)

According to the question,

(4y - 7x) = 4y$\times\frac{200}{3}$ %

⇒ (4y - 7x) = 4y$\times\frac{2}{3}$

⇒ 12y - 21x = 8y

⇒ 4y = 21x

⇒ y = 5.25x      -----(1)

Now, the ratio of the number of girls in A and B

⇒ (3y - 5x) : (4y - 7x)

⇒ (15.75x - 5x) : (21x - 7x)          [From equation (1)]

⇒ 10.75x : 14x

⇒ 43 : 56

∴  The ratio of the number of girls in A and B is 43 : 56.