"A certain sales target can be completed by a team of

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