Question

There are 105 people in a queue at a food stall. $\frac{4}{5}th$ of the people want to order burgers, $\frac{5}{7}th$ of the people want to order pizzas, and $\frac{15}{35}th$ of the people want to order fries. Arrange the food items according to their demand in ascending order.

• A. Fries > pizzas > burgers
• B. Pizzas < fries < burgers
• C. Fries < burger < pizzas
• D. Fries < pizzas < burgers

Answer 1

The correct option is D Fries < pizzas < burgers

The total number of orders is 105. To compare $\frac{4}{5},\frac{5}{7}$, and $\frac{15}{35}$, we need to make their denominators 105.
Fraction of people who want to order burgers:
$\frac{4}{5}=\frac{4\times 21}{5\times 21}=\frac{84}{105}$
Fraction of people who want to order pizzas:
$\frac{5}{7}=\frac{5\times 15}{7\times 15}=\frac{75}{105}$
Fraction of people who want to order fries:
$\frac{15}{35}=\frac{15\times 3}{35\times 3}=\frac{45}{105}$
$\frac{45}{105}<\frac{75}{105}<\frac{84}{105}$
Hence, the food items arranged in ascending order according to demand are: Fries < pizzas < burgers.