Question

The ratio of the number of boys to that of girls in a class is 1:3. After a certain number of new students are admitted to the class, it is found that the ratio of boys to girls still remains the same. How many new boys and girls might have been admitted?
a) 1 boy, 1 girl
b) 1boy, 3 girls
c) 3 boys, 1 girl
d) 3 boys, 3 girls

Answer 1

Answer:

D

Step-by-step explanation:

Answer 2

Answer:

The correct answer is option(b) 1boy, 3 girls

Step-by-step explanation:

Given,

The ratio of the number of boys to the number of girls in the class = 1:3

Then, the number of boys in the class = x

The number of girls in the class = 3x

Let 'a' be the number of new boys admitted and 'b' be the number of new girls admitted

Since the ratio remains the same  after adding 'a' boys and 'b' girls we have

x+a : 3x +b = 1:3

$\frac{x+a}{3x+b} = \frac{1}{3}$

Taking  3 out in the numerator we get

$\frac{x+a}{3(x+b/3} = \frac{1}{3}\\\\\frac{x+a}{x+b/3} = 1$

x+a = x+b/3

a = b/3

b = 3a

That the number of girls admitted newly is 3 times the number of boys admitted

Hence from the options this is true only for option (b)

Hence, the correct answer is option(b)

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