4 men and 6 woman can complete a work in 8 days, while 3 men and 7 woman can comp,ete in 10 days .In how many days will 10 woman complete it?

• Work done by 1 man in 1 day = M • Work done by 1 woman in 1 day = W Equation (1): 4M + 6W = 1/8  (because they finish 1 job in 8 days) Equation (2): 3M + 7W = 1/10  (because they finish 1 job in 10 days) Multiply (1) by 10 and (2) by 8 to remove denominators: (1) → 40M + 60W = 10/8 = 1.25 (2) → 24M + 56W = 8/10 = 0.8 Now subtract (2) from (1): (40M − 24M) + (60W − 56W) = 1.25 − 0.8 16M + 4W = 0.45 → 4M + W = 0.1125 (Equation 3) 4M + 6W = 1/8 = 0.125 Substitute 4M = 0.1125 – W So, (0.1125 − W) + 6W = 0.125 → 0.1125 + 5W = 0.125 → 5W = 0.0125 → W = 0.0025 Work done by 10 women per day = 10 × W = 10 × 0.0025 = 0.025 So, Days = 1 ÷ 0.025 = 40 days