50 people consume 350 kg of rice in 30 days. In how many days will 35 people consume 50 kg of rice ?

Answer: Option E

Let the required number of days be x
Less people, More days (Indirect proportion)
Less quantity, Less days ( Direct proportion)
$$\begin{array}{c}\text{People 35}:50\text{hfill}\\ \text{Quantity 350}:50\text{hfill}\end{array}\}::30:x$$
$$\begin{array}{rl}& \therefore 35\times 350\times x=50\times 50\times 30\\ & \iff x=\frac{\left(50\times 50\times 30\right)}{\left(35\times 350\right)}\\ & \iff x=\frac{300}{49}\\ & \iff x=6\frac{6}{49}\end{array}$$