Question
"A certain sales target can be completed by a team of
both men and womens in 60 days. If you replace eight womens with eight men, the same target can be accomplished in 75 days. If you further substitute five womens with five men in the original team,determine the time it takes for them to complete 70% of the sales target."Solution
ATQ, Let the total sales target will be 300 units {LCM (60 and 75)} Let the efficiency of each man and each women be 'a' units/day and 'b' units/day, respectively. Let number of men and number of women in the original group be 'm' and 'w', respectively. ATQ; ma + wb = (300/60) So, ma + wb = 5 ...... (I) Also, a × (m + 8) + b × (w - 8) = (300/75) Or, ma + 8a + wb - 8b = 4 Or, ma + wb + 8(a - b) = 4 Using equation (I), we have; 5 + 8 × (a - b) = 4 Or, (a - b) = (-1/8) ........ (II) Hence required time = (300 × 0.7) ÷ {a × (m + 5) + b × (w - 5)} = 210 ÷ {ma + 5a + wb - 5b} = 210 ÷ {ma + wb + 5 × (a - b)} = 210 ÷ {5 + 5 × (-1/8)} = 210 ÷ (35/8) = 48 days
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