Final answer:
To divide the payment of Rs 1120, we calculate the daily work rate of workers A and B, combine these rates, and find the proportion of total work each did, resulting in Rs 480 for A and Rs 640 for B.
Step-by-step explanation:
To calculate the share of the payment for each worker A and B, we first determine the rate at which they work individually and then combine these to find the rate at which they work together. Worker A can dig a trench in 6 days, which means A digs 1/6 of the trench per day. Worker B can dig a trench in 8 days, so B digs 1/8 of the trench per day.
Working together, they combine their daily rates to dig 1/6 + 1/8 = 7/24 of the trench per day. Hence, they can dig the entire trench in 24/7 days. The total payment for the trench is Rs 1120. To find each person's share, we calculate the proportion of the total work each did. A's share would be (1/6)/(7/24) of Rs 1120 and B's share would be (1/8)/(7/24) of Rs 1120.
Therefore, A's share is Rs 480 and B's share is Rs 640.