If 5 boys can do the decoration of whole school in 7 days and 9 boys can check the other arrangements for the party in 12 days, and if all of the 14 boys start working from 19^th July, when will the whole work be finished?

Using the LCM method, let the total work be 84 units. The first group of 5 boys has an efficiency of 12 units per day, while the second group of 9 boys has an efficiency of 7 units per day. Together, all 14 boys have an efficiency of 19 units per day, meaning they complete 57 units in the first 3 days. The remaining 27 units are completed on the 4th day, so starting from 19th July, the work finishes 4 days later on 29th July.

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