The weight of $A$ is $40\%$ greater than the weight of $B$ but $30\%$ less than the weight of $C$. What is the ratio of the weight of $B$ to the weight of $C$ expressed as a common fraction?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The weight of $A$ is $40\%$ greater than the weight of $B$ but $30\%$ less than the weight of $C$. What is the ratio of the weight of $B$ to the weight of $C$ expressed as a common fraction?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac12
The weight of $A$ is $40\%$ greater than the weight of $B$ but $30\%$ less than the weight of $C$. What is the ratio of the weight of $B$ to the weight of $C$ expressed as a common fraction?
train