Question
A certain number of women can complete a piece of work
in 9 days. If there were 18 women less, it would take 6 days more to complete the same work. If (x – 5) children and 5 men can complete a work in 20 days, while (x – 15) children and 30 men can complete the same work in 10 days, then find how many days are required to complete the same work by 84 men.Solution
ATQ, Originally, there would be x women. x * 9 = (x – 18) * 15 9x = 15x – 270 6x = 270 x = 45 Now, ( (45 – 5)C + 5M ) * 20 = ( (45 – 15)C + 30M ) * 10 (40C + 5M) * 20 = (30C + 30M) * 10 Divide both sides by 10, (40C + 5M) * 2 = 30C + 30M 80C + 10M = 30C + 30M 50C = 20M C = (2/5)M Total work = (40C + 5M) * 20 = (40 * 2/5 M + 5M) * 20 = (16M + 5M) * 20 = 21M * 20 = 420M Time required by 84 men = 420M / 84M = 5 days
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