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The ratio of the number of boys to the number of girls in a school of 1440 students is 7:5. If 40 new boys are admitted, then how many new girls may be admitted to make this ratio 4:3?

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160

754

880

answer is A.

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Detailed Solution

Given:
Total number of students = 1440
The ratio of the number of boys to the number of girls =

7 : 5

Let the number of boys be 7x and the number of girls is 5y.
So, from the question, we can say that

7 x + 5 y = 1440

………(i)
Now, by solving equation (i) we get the value of x. That is

\Rightarrow 7 x + 5 x = 1440

\Rightarrow 12 x = 1440

\Rightarrow x = \frac{1440}{12}

\Rightarrow x = 120

Now by using the value of x, we will get the number of boys and girls in the school. That is
Number of boys in the school

= 7 x

= 7 (120)

= 840

Number of girls in the school

= 5 x

= 5 (120)

= 600

Therefore, the number of boys and girls in the school is 840 and 600 respectively.
Now, according to the question, 40 new boys are admitted to the school which means now the total number of boots in the school is

840 + 40

.
And we have to find the number of new girls admitted to the school. Such that the ratio became

4 : 3

.
Let, the number of girls admitted be y. Therefore, the total number of girls in the school is

600 + y

And it is given in the question that after admitting 40 new boys and y new girls in the school the number of ratio of boys to the number of girls is

4 : 3

. So,

\Rightarrow \frac{840 + 40}{600 + y} = \frac{4}{3}

\Rightarrow \frac{880}{600 + y} = \frac{4}{3}

\Rightarrow (880) \times 3 = 4 \times (600 + y)

{By cross multiplication}

\Rightarrow 2640 = 2400 + 4 y

\Rightarrow 2640 - 2400 = 4 y

\Rightarrow 240 = 4 y

\Rightarrow \frac{240}{4} = y

\Rightarrow 60 = y

Thus, the number of new girls admitted to the school to make the ratio

4 : 3

is 60.

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