Question
A set of Q men can complete a work in 20 days, while
(Q+4) women can complete the same work in 28 days. If 9 men and 13 women together can finish the same work in 7 days, find Q.Solution
ATQ,
Qm × 20 = (Q+4)w × 28
5Qm = 7(Q+4)w
m/w = (7Q+28) / 5Q
Now,Q × (7Q+28) × 20 = [9 × (7Q+28) + 13 × 5Q] × 7
140Q² + 560Q = 63Q + 252 + 65Q
140Q² - 128Q - 252 = 0
70Q² - 64Q - 126 = 0
70Q² - 70Q + 6Q - 126 = 0
10Q(7Q - 7) + 6(7Q - 7) = 0
(7Q - 7)(10Q + 6) = 0
Q = 7/7, -6/10
Q = 1
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