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04. men and 12 boys can complete a work in 10 days while 6 men and8 boys can complete it in 14 days. The time taken by one man aloneto complete the work is(1) 70 days (2) 140 days (3) 280 days (4) 210 days |
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Answer» Let the time taken by man be x daysLet time taken by boys be y days work done by 1 man in one day = 1/x work done by 1 boy in one day = 1/y 8/x+12/y = 1/10.........eq(1) 6/x+ 8/y = 1/14..........eq(2) Let u=1/x & v=1/y 8u + 12v = 1/10............eq(3) 6u + 8v = 1/14..............eq(4) Multiplying eq(3) by 2 & eq(4) by 3 16u + 24v = 2/10.........eq(5) 18u + 24v = 3/14.........eq(6) subtract eq(5) - eq(6) -2u = -3/14 + 2/10-2u = (-3×10 + 2×14)/140-2u = (-30 + 28)/140-2u = -2/140u = 1/140 put this value in eq(5) 16u + 24v = 2/1016×1/140 + 24v = 1/54/35 + 24v = 1/524v = 1/5 - 4/3524v = (1×7 - 4)/3524v = (7 - 4)/3524v = 3/35v = 3/35×24v = 1/280 Now, u = 1/x1/140 = 1/xx = 140 v = 1/y1/280 = 1/yy = 280 Therefore, A man complete the work in 140 days. A boy can complete the work in 280 days. |
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