Question

In a school of $720$ students, the ratio of the no. of boys to the no. of girls is $3:5.$ If $18$ new girls are admitted in the school, then find how many new boys may be admitted so that the ratio of the no. of boys to the no. of girls may change to $2:3.$

• A. $84$
• B. $24$
• C. $63$
• D. $42$

Answer 1

The correct option is D $42$

Sum of the terms in the given ratio is $=3+5=8$
So, no. of boys in the school = $720\times \frac{3}{8}$= 270
No. of girls in the school = $720\times \frac{5}{8}$$=450$
Given that the number of new girls admitted in the school is 18 .
Let $x$ be the no. of new boys admitted in the school.
After the above new admissions,

No. of boys in the school $=270+x$
No. of girls in the school $=450+18=468$
Given : The ratio after the new admission is $2:3.$
Then, we have
$(270+x):468=2:3$
Use cross product rule$:3(270+x)=468\times 2$
$810+3x=936$
$3x=126$
$x=42$
So, the number of new boys admitted in the school is $42.$