Question

A bag contains tomatoes that are either green or red. The ratio of green tomatoes to red tomatoes in the bag is $4$ to $3$. When five green tomatoes and five red tomatoes are removed, the ratio becomes $3$ to $2$. How many red tomatoes were originally in the bag?

• A. $14$
• B. $15$
• C. $18$
• D. $24$
• E. $30$

Answer 1

Answer: (B)

$15$

Ratio of green tomatoes to red is $4:3$.
Let number of green tomatoes be $4n$ and red tomatoes be $3n$
When $5$ tomatoes are removed from each, then the ratio becomes $3:2$.
As per problem,
$\frac{4n-5}{3n-5}=\frac{3}{2}$
$\Rightarrow 8n-10=9n-15$
$\Rightarrow 8n-9n=-15+10$
$\Rightarrow -n=-5$
$\Rightarrow n=5$
Originally $3\times 5=15$ tomatoes were in the bag.