A sum of ₹ 750 is distributed among $A$, $B$, $C$ and $D$ in such a manner that $A$ gets as much as $B$ and $C$ together, $B$ gets ₹ 125 more than $C$ and $D$ gets as much as $C$. What is $A$'s share?

## Concept & Logic This requires translating English statements into simultaneous algebraic equations. The key strategy is to find a common "base" variable (in this case, $C$) and express every other person's share in terms of that base variable. $$ Total = A + B + C + D $$ ## Step-by-Step Solution * **Given:** Total sum = 750. Equation 1: $A = B + C$ Equation 2: $B = C + 125$ Equation 3: $D = C$ * **Deduction:** We can express $A$, $B$, and $D$ strictly in terms of $C$. We already have $B$ and $D$. Let's substitute $B$ into Equation 1 to find $A$: $A = (C + 125) + C = 2C + 125$ * **Calculation:** Substitute all expressions into the total sum equation: $(2C + 125) + (C + 125) + C + C = 750$ * **Calculation:** Combine like terms: $5C + 250 = 750$ $5C = 500$ $C = 100$ * **Calculation:** The question asks for $A$'s share. Substitute $C = 100$ into the expression for $A$: $A = 2(100) + 125 = 200 + 125 = 325$ ## Exam Strategy & Shortcut You can solve this purely via logical substitution on paper without formal equations. Think: $A, B, C, D$. $C$ is the baseline. $D$ is the same as $C$. $B$ is $C + 125$. $A$ is $B + C = 2C + 125$. Total sum consists of 5 parts of $C$ plus 250 extra (from $A$ and $B$). $5C + 250 = 750 \rightarrow 5C = 500 \rightarrow C = 100$. $A = 2C + 125 = 325$. Very quick mental math. ## Common Pitfall Misinterpreting "gets as much as B and C together" as $A = B = C$. It strictly means $A = B + C$. Reading carefully is critical to setting up the initial linear relationships correctly. ## Final Answer Therefore, the correct answer is **₹ 325**.