Anand, Bijoy, Chetan and Dharma together have ₹ 47 with them. Anand and Bijoy together have ₹ 27; Chetan and Anand have ₹ 25 and Dharma and Anand have ₹ 23. How much money does Bijoy have?

## Concept & Logic This is a system of linear equations where one variable (Anand) acts as a common link across multiple subset sums. Summing the overlapping equations allows us to extract the value of the common variable efficiently. $$ Sum\ of\ Subsets = Multiplier \times Common\ Variable + Total\ Sum $$ ## Step-by-Step Solution * **Given:** Let their money be $A, B, C, D$. Total: $A + B + C + D = 47$ Equation 1: $A + B = 27$ Equation 2: $C + A = 25$ Equation 3: $D + A = 23$ * **Calculation:** Add Equations 1, 2, and 3 together: $(A + B) + (C + A) + (D + A) = 27 + 25 + 23$ $3A + B + C + D = 75$ * **Substitution:** We know that $A + B + C + D = 47$. We can rewrite our summed equation as: $2A + (A + B + C + D) = 75$ $2A + 47 = 75$ * **Calculation:** Solve for $A$ (Anand): $2A = 75 - 47$ $2A = 28$ $A = 14$ * **Calculation:** The question asks for Bijoy's money ($B$). Substitute $A$ into Equation 1: $14 + B = 27 \implies B = 13$ ## Exam Strategy & Shortcut Add the three partial sums: $27 + 25 + 23 = 75$. Notice that this sum counts Anand ($A$) three times, while counting everyone else ($B, C, D$) exactly once. So, $Sum = 2A + Total$. $75 = 2A + 47 \implies 2A = 28 \implies A = 14$. Since $A + B = 27$, Bijoy ($B$) is simply $27 - 14 = 13$. This can be done mentally in seconds. ## Common Pitfall Attempting to solve for each individual person ($C$ and $D$) before answering the question. This wastes valuable exam time. Always focus strictly on finding the specific variable requested (in this case, $B$, which only requires finding $A$). ## Final Answer Therefore, the correct answer is **₹ 13**.