Question

The ratio of bots to girls in a school of 1430 students is 7:6 . If 26 new girls are admitted in the school, find out 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:

Step-by-step explanation:

new boys may be admitted so that the ratio of number of boys to the number of girls may change to 8:7.

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

$\textbf{\underline{Total\;no\;of\;Students}}$

= 1430

$\textbf{\underline{Past\;ratio\;of\;Boys\;and\;Girls}}$

= 7 : 6

$\textbf{\underline{Combined\;Ratio}}$

= 7 + 6

= 13

$\textbf{\underline{No\;of\;boys}}$

$\tt{\rightarrow\dfrac{7\times 1440}{13}}$

$\tt{\rightarrow\dfrac{10010}{13}}$

= 770

Hence,

$\textbf{\underline{No\;of\;Boys}}$

= 770

$\textbf{\underline{No\;of\;Girls}}$

$\tt{\rightarrow\dfrac{6\times 1430}{13}}$

$\tt{\rightarrow\dfrac{8580}{13}}$

Hence,

$\textbf{\underline{No\;of\;Girls}}$

= 660

$\textbf{\underline{Girls\;Admitted}}$

= 26

Therefore,

$\textbf{\underline{No\;of\;girls\;after\;admission\;of\;26\;girls}}$

= 660 + 26

= 686

Assume

$\textbf{\underline{No\;of\;boys\;admitted\;be\;p}}$

Hence,

$\textbf{\underline{Total\;No\;of\;boys}}$

= (770 + p)

$\textbf{\underline{Re\;Ratio=8:7}}$

$\tt{\rightarrow\dfrac{770+p}{686}=\dfrac{8}{7}}$

(770 + p) × 7 = 686 × 8

5390 + 7p = 5488

7p = 5488 - 5390

7p = 98

$\tt{\rightarrow p=\dfrac{98}{7}}$

p = 14

Therefore,

$\tt{\boxed{Admitted\;=\;14\;boys\;ratio\;changes\;to\;8:7}}$