The sum of the salaries of A and B is ₹ 2100. A spends 80% of his salary and B spends 70% of his salary. If their savings are in the proportion of 4 : 3, then what is the salary of A?

### Concept & Ratio of Savings When given the total sum of two variables and the ratio of their remaining parts (savings), express the remaining parts as percentages of the original variables and equate them to the given ratio. $$ \frac{S_A}{S_B} = \frac{4}{3} $$ ### Step-by-Step Solution * **Given:** Total salary = $₹ 2100$. Ratio of savings = $4 : 3$. * Let the salary of $A$ be $x$. * The salary of $B$ will be $(2100 - x)$. * $A$ spends $80\%$, so $A$ saves $20\%$ of his salary. * $B$ spends $70\%$, so $B$ saves $30\%$ of his salary. * Expressing their savings as a ratio: $$ \frac{0.20x}{0.30(2100 - x)} = \frac{4}{3} $$ * Simplify the decimals: $$ \frac{2x}{3(2100 - x)} = \frac{4}{3} $$ * Cross-multiply: $$ 6x = 12(2100 - x) $$ $$ 6x = 25200 - 12x $$ $$ 18x = 25200 $$ * Solve for $x$: $$ x = \frac{25200}{18} = 1400 $$ * Thus, the salary of $A$ is $₹ 1400$. ### Exam Strategy & Shortcut Instead of solving the full linear equation, work with the simplified fraction: $\frac{2x}{6300 - 3x} = \frac{4}{3}$. From here, test the options. If $A = 1400$, then $20\%$ of $1400 = 280$. $B = 2100 - 1400 = 700$, and $30\%$ of $700 = 210$. The ratio $280 : 210 = 28 : 21 = 4 : 3$, which matches instantly. ### Common Pitfall A frequent error is calculating the ratio of their *expenditures* instead of their *savings*. Always carefully read whether the given ratio applies to what they spent or what they kept. ### Final Answer Therefore, the correct answer is **₹ 1400**.