₹ 1050 are divided among $P$, $Q$ and $R$. The share of $P$ is $\frac{2}{5}$ of the combined share of $Q$ and $R$. $P$ gets

### Concept & Proportional Division When one part is given as a fraction of the remaining sum, you can establish a direct ratio between that part and the total sum. ### Step-by-Step Solution Given: * Total amount = $P + Q + R = 1050$ * $P = \frac{2}{5}(Q + R)$ 1. From the second equation, we can find the ratio of $P$ to the sum of $(Q+R)$: $\frac{P}{Q+R} = \frac{2}{5}$ 2. This means if $P$ gets 2 parts, $Q+R$ gets 5 parts. 3. The total parts for the whole amount ($P+Q+R$) is $2 + 5 = 7$ parts. 4. So, $P$'s share is $\frac{2}{7}$ of the total amount. 5. $P = \frac{2}{7} \times 1050$ 6. $P = 2 \times 150 = 300$ ### Exam Strategy & Shortcut Recognize instantly that $P = \frac{2}{5}(Q+R)$ means $P$ is $2$ parts out of a total of $2+5=7$ parts. Calculate $1050 \times \frac{2}{7} = 300$ in one step. ### Common Pitfall Trying to find the individual values of $Q$ and $R$. The problem doesn't provide enough information for that, and it is unnecessary to find $P$'s share. ### Final Answer Therefore, the correct answer is **₹ 300**.