Question

The ratio of number of students studying Arts, Commerce and science in a college is $3:5:8$. What is the new ratio of the number of students studying Arts, Commerce and science respectively, if there is an increase of $20\%$, $40\%$ and $25\%$ in the number of students studying Arts, Commerce, and Science.

• A. $35:18:50$
• B. $18:50:35$
• C. $20:18:50$
• D. $18:35:50$

Answer 1

The correct option is D $18:35:50$

Arts:commerce:science$=3:5:8$

Let the common ratio be $x$

$\therefore$ No. of in Arts $=3x$

$\therefore$ No. of in commerce $=5x$

$\therefore$ No. of in science $=8x$

increase in arts students $=20\%$

$\therefore$ New No. of students in Arts $= 3x(1+\frac{20}{100})$

$=\frac{360x}{100}$

increase in commerce students $=40\%$

$\therefore$ New No. of students in commerce $=5x(1+\frac{40}{100})$

$=\frac{700x}{100}$

increase in science students $=25\%$

$\therefore$ New No. of students in science $=8x(1+\frac{25}{100})$

$=\frac{1000x}{100}$

$\therefore$ new ratio of Arts:commerce:science

$=\frac{360x}{100}:\frac{700x}{100}:\frac{1000x}{100}$

$=36x:70x:100x$

$=18:35:50$