Question

At a certain college, the ratio of freshmen to sophomores is $2:3$ and the ratio of sophomores to juniors is the ratio of 5 : 6 . If the ratio of juniors to seniors is 3 : 5. What is the ratio of freshmen to seniors?

• A. $1:3$
• B. $5:9$
• C. $3:5$
• D. $4:7$
• E. $5:6$

Answer 1

The correct option is A $1:3$

Given,

$\frac{freshmen}{sophomores}=\frac{2}{3}=\frac{10}{15}$ ------ (i)

$\frac{sophomores}{juniors}=\frac{5}{6}=\frac{15}{18}$ ------ (ii)

$\frac{juniors}{seniors}=\frac{3}{5}=\frac{18}{30}$ ------ (iii)

(i)$\times$(ii) gives,

$\frac{freshmen}{sophomores}\times \frac{sophomores}{juniors}=\frac{10}{15}\times \frac{15}{18}$

$\frac{freshmen}{juniors}=\frac{10}{18}$ ------ (iv)

(iv)$\times$(iii) gives,

$\frac{freshmen}{juniors}\times \frac{juniors}{seniors}=\frac{10}{18}\times \frac{18}{30}$

$\frac{freshmen}{juniors}=\frac{10}{30}=\frac{1}{3}$

Option A