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Question

8 women and 12 girls can finish a piece of work in 10 days while 6 women and 8 girls can finish it in 14 days find the time taken by 1 women alone and by that of one girl alone to finish the same work

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Solution

Let 1 woman finish the work in x days and 1 man finish the work in y days. work done by 1 woman in 1 day = 1/x work done by 1 man in 1 day = 1/y ATQ Case 1: 8 women and 12 men finish work in 10 days 1 day’s work of 8 women and 12 men= 1/10 part of work. 8/x + 12/y = 1/10 4(2/x + 3/y) = 1/10 2/x + 3/y = 1/40……….(1) Case 2. 6 women and 8 men finish work in 14 days 1 day’s work of 6 women and 8 men= 1/14 part of work. 6/x + 8/y = 1/14 2(3/x + 4/y) = 1/14 3/x + 4/y = 1/28……….(2) Putting 1/x = p and 1/y = q in equations,1 & 2 , 2p + 3q = 1/40………….(3) 3p + 4q = 1/28………….(4) Multiply equation 3 by 4 and equation 4 by 3, 8p + 12q = 4/40 8p +12q = 1/10…………..(5) 9p + 12q = 3/28………….(6) On subtracting equation 5 and 6, 8p +12q = 1/10 9p + 12q = 3/28 (-) (-) (-) ----------------- - p = 1/10-3/28 -p = (14 - 15)/140 -p = -1/140 p = 1/140 On substituting p= 1/140 in equation 5, 8p +12q = 1/10 8(1/140) +12q = 1/10 8/140 + 12q = 1/10 12q = 1/10 - 2/35 12q = (7 - 4)/70 12q = 3/70 q= 3/(70×12) q= 1/(70×4) q= 1/280 Now p= 1/140= 1/x x = 140 q= 1/280= 1/y y = 280 Hence, the time taken by one woman alone to finish the work = 140 days and one man alone to finish the work = 280 days. ii)Removal of gender discrimination & woman Can work faster than man.

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