Raman and Raju undertook a work for Rs. 5500. Raman alone can do that work in 5 days and Raju alone can do the same work in 6 days. If they work together, then what will be the difference in the amount they receive?

Let the total work be one complete job (unit work).

Raman’s rate of work = $$\frac{1}{5}$$ job per day (because he finishes the job in 5 days).
Raju’s rate of work = $$\frac{1}{6}$$ job per day (because he finishes the job in 6 days).

When they work together, both are on the job for the same amount of time. Therefore, the share of money each should get is proportional to the amount of work each does, which in turn is proportional to their respective working rates.

Ratio of their rates = $$\frac{1}{5} : \frac{1}{6} = 6 : 5$$ (multiplying both terms by 30 to clear denominators).

Hence Raman : Raju = 6 : 5.

Total payment = Rs. 5500.
Sum of ratio terms = $$6 + 5 = 11$$ parts.

Value of one part = $$\frac{5500}{11} = 500$$ rupees.

Raman’s share = $$6 \times 500 = \text{Rs. }3000$$.
Raju’s share = $$5 \times 500 = \text{Rs. }2500$$.

Difference in the amounts = $$3000 - 2500 = \text{Rs. }500$$.

Option A which is: Rs. 500