₹ 16000 are to be distributed between B and A such that B gets ₹ 4000 less than A. The ratio of the amount received by A to that received by B is

### Concept & Linear Equations To find individual shares from a total sum when their difference is given, we can set up a simple linear equation. ### Step-by-Step Solution * Let the amount received by $A$ be $x$. * Since $B$ gets ₹ 4000 less than $A$, the amount received by $B$ is $x - 4000$. * The total amount distributed is ₹ 16000. So, $x + (x - 4000) = 16000$. * $2x - 4000 = 16000$ * $2x = 20000 \implies x = 10000$ * Amount received by $A$ is ₹ 10000. * Amount received by $B$ is $10000 - 4000 = 6000$. * The ratio of the amount received by $A$ to $B$ is $10000 : 6000 = 10 : 6 = 5 : 3$. ### Exam Strategy & Shortcut Instead of algebraic equations, use logical deduction: If you remove the ₹ 4000 difference from the total ₹ 16000, you are left with ₹ 12000. Divide this equally to get ₹ 6000 each. Give the extra ₹ 4000 to $A$. Thus, $A$ gets 10000 and $B$ gets 6000. The ratio is $10000:6000 = 5:3$. ### Common Pitfall Misreading the question and finding the ratio of $B$ to $A$ instead of $A$ to $B$, leading to the incorrect option 3 : 5. ### Final Answer Therefore, the correct answer is **5 : 3**.