Discussion
Rice and wheat are in a mixture in the ratio 5:3. If 16 kg wheat is added to this mixture, the ratio of rice to wheat changes to 5:7. How much wheat is in new mixture?
Answer: B
Let rice \( = 5k \) and wheat \( = 3k \). Adding 16 kg of wheat changes only the wheat.
\[ \frac{5k}{3k + 16} = \frac{5}{7} \quad\Longrightarrow\quad 35k = 15k + 80 \]
\[ 20k = 80 \quad\Longrightarrow\quad k = 4 \]
\[ \text{new wheat} = 3(4) + 16 = 28 \text{ kg} \]
The question asks for the wheat in the new mixture, not the original 12 kg.
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