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2 women and 5 men can together finish a piece of embroidery in 4 days, while 6 men and 3 women can finish it in 3 days. Find the time taken by 1 woman alone to finish the embroidery and that taken by a man alone.plz answer fast and give step to step explanation |
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Answer» Answer: 18 & 36 DAYS respectively. Step-by-step explanation: Let w and m represent women and men respectively 2W + 5M can do 1 work in 4 days 2W + 5M can do 1/4 work in 1 days Also, 3W + 6M can do 1 work in 3days 3W + 6M can do 1/3 work in 1day Then, equating work with men and women 2W + 5M =1/4.(i) Then, 3W + 6M=1/3-(II) Or, 3(W + 2M)=1/3 Or,W + 2M =1/9-(iii) Then subtracting (i) from (ii) 3W + 6M=1/3 -2W - 5M =-1/4) W + M=1/3 -1/4 W + M= 1/12...............(iv) Also, Subtracting (iv) from (iii) W + 2M =1/9 -W - M=-1/12 M = 1/9 – 1/12 Or, M=1/36 So subsituting m=1/36 in equation (iv) W + 1/36 = 1/12 Or,W = 1/12 – 1/36 Hence, W=1/18 I men alone can do (1/36) work in 1 day 1 men alone can do 1 work in 36 days Also, 1 women alone can do (1/18) in 1 day 1 women alone can do 1 work in 18 days |
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