Question
A group of 6 men and 5 women can finish a certain task
in 8 days, while another group of 3 men and 15 women can complete the same task in 6 days. Now, 4 men and 3 women have worked on the task for 6 days. How many additional women are needed to ensure the remaining work is completed in the next 3 days?Solution
According to question: 8 × (6M + 5W) = 6 × (3M + 15W) 48M + 40W = 18M + 90W 30M = 50W 3M = 5W Let the amount of work done by a man in one day = 5 units So the amount of work done by a woman in one day = 3 units So the total work = 8 × (6 × 5 + 3 × 5) = 360 units Amount of work done by 4 men and 3 women in 6 days = 6 × (4 × 5 + 3 × 3) = 174 units Remaining work = 360 – 174 = 186 units Let ‘x’ more women are required to complete the remaining work in 3 days According to question: 3 × {4 × 5 + (3 + x) × 3} = 186 20 + 9 + 3x = 62 3x = 33, x = 11 So, 11 more women are required to complete the work in given time.
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