Question

the ratio of the number of boys to the number of girls in a school of 1430 students is 7/6.if 26 new girls are admitted in the school find how many new boys may be admitted so that the ratio of number of boys to the number of girls may change to 8/7​

Answer 1

Answer:

14 New Boys are admitted.

Step-by-step explanation:

Given :

• Total students in the school = 1430

To Find :

• New boys Admitted

Solution :

Case 1 :

Let the number of boys = x

So, number of girls = 1430 – x

According to the Given Condition,

$\frac{x}{1430 - x} = \frac{7}{6} \\ \\ \implies 6x = 7(1430 - x) \\ \\ \implies 6x = 10010 - 7x \\ \\ \implies 13x = 10010 \\ \\ \implies x = \frac{10010}{13} \\ \\ \implies x = 110$

So, Number of girls

= 1430 – 770

= 660

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Case 2 :

If 26 new girls are admitted, then

If 26 new girls are admitted, then Number of girls in the school

= 660 + 26

= 686

Let the number of boys to be admitted = y

So, According to the Given Condition,

$\frac{770 + y}{686} = \frac{8}{7} \\ \\ \implies 7(770 + y) = 5488 \\ \\ \implies 5390 + 7y = 5488 \\ \\ \implies 7y = 98 \\ \\ \implies y = \frac{98}{7} \\ \\ \implies y = 14$

Hence, 14 new boys were to be admitted to maintain the ratio of 8 : 7.

________________________

Thanks ..!!!

Answer 2

$\huge\bigstar\mathfrak\green{\underline{\underline{SOLUTION:}}}$

Total students in the school=1430

Case 1️⃣

let the number of boys=x

& number of girls= 1430-x

According to the given condition,

$= > \frac{x}{1430 - x} = \frac{7}{6} \\ = > 6x = 7 \times 1430 - 7x \\ = > 13x = 7 \times 1430 \\ = > x = \frac{7 \times 1430}{13} \\ = > x = 7 \times 110 \\ = > x = 770$

So, the number of girls=1430-770= 660.

Case 2️⃣

If 26 new girls are admitted, then number of girls in the school =)660+26=686.

Let the number of boys to be admitted=y

So, according to the given condition,

$= > \frac{770 + y}{686} = \frac{8}{7} \\ = > 5390 + 7y = 5488 \: \: \: (cross \: multiplication) \\ = > 7y = 5488 - 5390 \\ = > 7y = 98 \\ = > y = \frac{98}{7} = 14 \\ \\ = > y = 14$

Hence, 14 new boys were to be admitted to maintain the ratio of 8:7.

hope it helps ☺️