The rice 2

60 kg of a certain variety of rice at Rs 32 per kg is mixed with 48 kg of another variety of rice, and the mixture is sold at the average price of Rs 28 per kg. If there is no profit or loss due to the new sale price, then find the price of the second variety of rice.

Correct answer:

p₂ =  23 Rs/kg

Step-by-step explanation:

$$\begin{gathered} m_1=60\text{kg} \\ {m}_2=48\text{kg} \\ {p}_1=32\text{Rs/kg} \\ p=28\text{Rs/kg} \\ m=m_1+m_2=60+48=108\text{kg} \\ {m}_1\cdot p_1+m_2\cdot p_2=m\cdot p \\ {p}_2=\frac{m\cdot p-m_1\cdot p_1}{m_2}=\frac{108\cdot 28-60\cdot 32}{48}=23=23\text{Rs/kg} \\ \text{ Verifying Solution: } \\ P=\frac{p_1\cdot m_1+p_2\cdot m_2}{m_1+m_2}=\frac{32\cdot 60+23\cdot 48}{60+48}=28\text{Rs/kg} \end{gathered}$$

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