Question

There are 24 Rosagollas and 36 Kulfis in a box. Anil eats only Rosagollas at $x$ per minute, Anand eats only Kulfis at $y$ per minute, and Abhilash eats $2x$ Rosagollas and $3y$ Kulfis per minute. After two minutes, the number of Rosagollas and Kulfis left is equal. Find the ratio of Kulfis that Abhilash eats per minute to Rosagollas that Anil eats per minute.

• A. $\frac{2}{9}$
• B. $\frac{3}{2}$
• C. $\frac{9}{4}$
• D. $\frac{9}{2}$

Hint:

In rate problems, equate remaining quantities to form a linear equation in $x$ and $y$, then interpret the desired ratio.

Answer 1

The Correct Option is C

Rosagollas eaten per minute: Anil = $x$, Abhilash = $2x$ $\Rightarrow$ total = $3x$ per minute. In 2 minutes: $6x$ eaten. Remaining Rosagollas: $24 - 6x$. Kulfis eaten per minute: Anand = $y$, Abhilash = $3y$ $\Rightarrow$ total = $4y$ per minute. In 2 minutes: $8y$ eaten. Remaining Kulfis: $36 - 8y$. Given remaining are equal: \[ 24 - 6x = 36 - 8y \quad \Rightarrow \quad 8y - 6x = 12 \quad \Rightarrow \quad 4y - 3x = 6 \] Thus: \[ \frac{y}{x} = \frac{3x + 6}{4x} \] We need $\frac{3y}{x}$: \[ \frac{3y}{x} = 3 \cdot \frac{3x + 6}{4x} = \frac{9x + 18}{4x} \] Choosing smallest integer $x$ making $y$ integer gives $x=2$, $y=3$. Ratio = $\frac{9}{4}$. \[ \boxed{\frac{9}{4}} \]