A butcher sells $30\ kg$ beef with $40$% profit and sells $24\ kg$ chicken with $75$% profit. The butcher gains same profit from the both sales. What is ($1$ kg chicken price) / ($1$ kg beef price)?
- Since the question says both sales' profits are same, both sales' prices are same. Aren't they?
Let's say 1kg beef price is $10b$ and 1kg chicken price is $10c$.
$$30*10b*1.4 = 24*10c*1.75$$
$$420b = 420c$$ $$\frac cb = 1$$ is what I get as the result. But the answer says $\frac56$
What point did I get wrong?
We are given profit so we must consider prices and costs. Let $P_b, P_c, C_b$ and $C_c$ be the prices and costs of beef and chicken, respectively.
Then we are told that we make $40\%$ profit on the sale of beef and $75\%$ profit on the sale of chicken. We are also told the total profits are equal so we get $$30(0.4C_b)=24(.75)C_c\implies 12C_b=18C_c\implies C_b=\frac{3}{2}C_c$$
The profit on beef is $$P_b-C_b=P_b-\frac{3}{2}C_c=\frac{2}{5}\cdot\frac{3}{2}C_c$$ which imples $$P_b=\frac{21}{10}C_c$$
Likewise, the profit on chicken is $$P_c-C_c=\frac{3}{4}C_c$$ which implies $$P_c=\frac{7}{4}C_c$$
Dividing $P_c$ by $P_b$ gives the result.