Laxman, Madan and Naman started a piece of work. They worked on it for 5 days, after which Laxman left. The other two continued to work for 5 more days after which Madan left and the remaining work was completed by Naman in 5 more days. If Madan alone can complete the work in 30 days and Naman alone takes more than 45 days to complete the work, then which of the following is true?

Let the total work be 1 unit, and let the daily work rates of Laxman, Madan, and Naman be l, m, and n respectively. Madan's rate m is 1 divided by 30, and since Naman takes more than 45 days, his rate n is less than 1 divided by 45. The total work equation is 5 times the sum of l, m, and n plus 5 times the sum of m and n plus 5 times n, which simplifies to 5l plus 10m plus 20n equals 1. To satisfy this equation with a low n, l must be relatively large, meaning Laxman did the greatest part of the work.

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