Question

Which ratio is smallest 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 $\Rightarrow \frac{13}{27}$

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

146: 297 $\Rightarrow \frac{146}{297}$

157 : 297 $\Rightarrow \frac{157}{297}$

LCM of denominators 27 and 33 and 297 = 297

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

Multiply and divide $\frac{17}{33}$ by 9 . we get :

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

Hence the required ratio is $\frac{143}{297}$ , $\frac{153}{297}$, $\frac{146}{297}$ , $\frac{157}{297}$

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