A and B together have Rs. 9000. If \(\frac{4}{11}\) of A's amount is equal to \(\frac{3}{5}\) of B's amount, how much amount does A have?

Solution

Given \(\frac{4}{11}A=\frac{3}{5}B\). Cross-multiplying gives \(20A=33B\), so \(A:B=33:20\). The total ratio is \(53\). Therefore, \(A=\frac{33}{53}\times9000=5603.7735\ldots\)₹, approximately Rs. 5603.8. Trick: Convert the fractional equality into a ratio, then divide the total amount in that ratio.