Let's analyze the problem step-by-step.

Problem:

• A can complete the work in 12 days.
• B can complete the work in 10 days.
• The total payment for the work is Rs. 220.
• A and B work together.
• Find A's share of the payment.

Step 1: Calculate the work rates of A and B

• A's work rate = 1 work / 12 days = 112\frac{1}{12}121​ work per day.
• B's work rate = 1 work / 10 days = 110\frac{1}{10}101​ work per day.

Step 2: Calculate their combined work rate

Combined work rate = A's rate + B's rate

112+110=560+660=1160\frac{1}{12}+\frac{1}{10}=\frac{5}{60}+\frac{6}{60}=\frac{11}{60}121​+101​=605​+606​=6011​ work per day.

Step 3: Calculate the share of work done by A and B

• A's share of work = 1/1211/60=112×6011=511\frac{1/12}{11/60}=\frac{1}{12}\times \frac{60}{11}=\frac{5}{11}11/601/12​=121​×1160​=115​
• B's share of work = 1/1011/60=110×6011=611\frac{1/10}{11/60}=\frac{1}{10}\times \frac{60}{11}=\frac{6}{11}11/601/10​=101​×1160​=116​

Step 4: Calculate A's share of the payment

Total payment = Rs. 220
A's share = 511×220=5×20=Rs.100\frac{5}{11}\times 220=5\times 20=Rs.100115​×220=5×20=Rs.100

Answer:

A's share of the payment is Rs. 100.