To do a certain work, the ratio of efficiency of A to that of B is 3 : 7. Working together, they can complete the work in 10.5days. They work together for 8 days. 60% of the remaining work will be completed by A alone in?Options6.5 days5 days4 days5.5days
Question
To do a certain work, the ratio of efficiency of A to that of B is 3 : 7. Working together, they can complete the work in 10.5days. They work together for 8 days. 60% of the remaining work will be completed by A alone in?Options6.5 days5 days4 days5.5days
Solution
The problem can be solved in the following steps:
Step 1: Understand the problem The problem states that the efficiency ratio of A to B is 3:7. This means that for every 10 units of work done, A does 3 units and B does 7 units. They can complete the work together in 10.5 days. They work together for 8 days and then A alone will complete 60% of the remaining work.
Step 2: Calculate the total work Since A and B can complete the work together in 10.5 days, and their combined efficiency is 10 units (3 for A and 7 for B), the total work is 10.5 * 10 = 105 units.
Step 3: Calculate the work done in 8 days In 8 days, A and B together can do 8 * 10 = 80 units of work. So, the remaining work is 105 - 80 = 25 units.
Step 4: Calculate the work A will do A will do 60% of the remaining work, which is 0.60 * 25 = 15 units.
Step 5: Calculate the time A will take Since A's efficiency is 3 units per day, A will take 15 / 3 = 5 days to complete 60% of the remaining work.
So, the answer is 5 days.
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