Question

Which ratio is smaller among $13:27,17:33,146:297,157:297$ ?

• A. $146:297$
• B. $157:297$
• C. $17:33$
• D. $13:27$

Answer 1

The correct option is D

$13:27$

Given : $13:27\Rightarrow$ $\frac{13}{27}$ and

$17:33\Rightarrow$ $\frac{17}{33}$

LCM of denominators $27$ and $33$ $=297$

we need to make denominators of $\frac{13}{27}$ and $\frac{17}{33}$ equal to LCM $297$

For that multiply the numerator and denominator of $\frac{13}{27}$ by $11$, we get :

$\frac{13}{27}=\frac{13\times 11}{27\times 11}=\frac{143}{297}$

Multiply the numerator and denominator of $\frac{17}{33}$ by $9$, we get :

$\frac{17}{33}=\frac{17\times 9}{33\times 9}=\frac{153}{297}$

Now we have all fractions with same denominator: $\frac{143}{297}$ , $\frac{153}{297}$ ,$\frac{146}{297}$ and $\frac{157}{297}$

Numerator: $143<146<153<157$

So, smaller fraction is $\frac{143}{297}$

$\frac{143}{297}=\frac{13}{27}$

$\frac{13}{27}$ $\Rightarrow 13:27$

Answer is : $13:27$