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QA – Placement Quizzes | Work and Wages | Question 7

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6 men and 10 women were employed to make a road 360 km long. They were able to make 150 kilometres of road in 15 days by working 6 hours a day. After 15 days, two more men were employed and four women were removed. Also, the working hours were increased to 7 hours a day. If the daily working power of 2 men and 3 women are equal, find the total number of days required to complete the work. (A) 19 (B) 35 (C) 34 (D) 50

Answer: (C)

Explanation: We are given that the daily working power of 2 men and 3 women are equal. => 2 Em = 3 Ew => Em / Ew = 3/2, where ‘Em’ is the efficiency of 1 man and ‘Ew’ is the efficiency of 1 woman. Therefore, ratio of efficiency of man and woman = 3 : 2. If ‘k’ is the constant of proportionality, Em = 3k and Ew = 2k. Here, we need to apply the formula ∑(Mi Ei) D1 H1 / W1 = ∑(Mj Ej) D2 H2 / W2, where ∑(Mi Ei) = (6 x 3k) + (10 x 2k) ∑(Mj Ej) = (8 x 3k) + (6 x 2k) D1 = 15 days D2 = Number of days after increasing men and reducing women H1 = 6 hours H2 = 7 hours W1 = 150 km W2 = 210 km   So, we have 38k x 15 x 6 / 150 = 36k x D2 x 7 / 210 => 38k x 6 = 12k x D2 => D2 = 19 days Therefore, total days required to complete the work = 15 + 19 = 34 days

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Last Updated : 28 Jun, 2021
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