Question

At a certain school, the ratio of the number of second graders to the number of fourth graders is $8$ to $5$, and the ratio of the number of first graders to the number of second graders is $3$ to $4$. If the ratio of the number of third graders to the number of fourth graders is $3$ to $2$, what is the ratio of the number of first graders to the number of third graders?

• A. $16$ to $15$
• B. $9$ to $5$
• C. $5$ to $16$
• D. $5$ to $4$
• E. $4$ to $5$

Answer 1

Answer: (E)

$4$ to $5$

Let me of first, second, third and fourth graders be denoted as $G_1,G_2,G_3$ and $G_4$ respectively of a school.

$G_2:G_4=8:5⟶\left(1\right)\left(1\right)÷\left(2\right)$

$G_1:G_2=3:4⟶\left(2\right)$

$G_3:G_4=3:4⟶\left(3\right)$

$G_1:G_3=?$

$G_1:G_4=6:5G3:G_4=3:2\Rightarrow \frac{\frac{G_1}{G_4}}{\frac{G3}{G_4}}=\frac{\frac{6}{5}}{\frac{3}{2}}=\frac{4}{5}$

$\Rightarrow G_1:G3=4:5$