The monthly income of A and B are in the ration of 4 : 5, and their monthly expenditures are in the ratio of 7 : 9. If each saves Rs. 50 per month, the monthly income of A is

Let A's and B's incomes be 4x and 5x, and their expenditures be 7y and 9y. Since each saves Rs. 50, we get 4x - 7y = 50 and 5x - 9y = 50. Solving these gives y = 50 and x = 100. So A's monthly income is 4 x 100 = Rs. 400, and option A is correct.

Check: A earns 400 and spends 350, saving 50. B earns 500 and spends 450, saving 50. Income ratio 400:500 = 4:5 and expenditure ratio 350:450 = 7:9.

• B (Rs. 500) is B's income, not A's. This is the number a candidate lands on by reading the wrong person.
• C (Rs. 512) and D (Rs. 530) fail the savings condition. With A = 512, B = 640, A's expenditure is 462 and B's would need to be 590 for B to save 50, but then B saves 46.

The core concept is simultaneous linear equations built from ratios, a standard quantitative aptitude tool that appears in UPPSC Prelims General Studies and CSAT-style papers. Substituting the options into the equations is a fast verification method.

Trap: Stopping after finding x = 100 and reporting B's income (500) instead of A's (400).