Last updated at July 24, 2021 by Teachoo

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Ex 3.6, 2 (Introduction) Formulate the following problems as a pair of equations, and hence find their solutions: (ii) 2 women & 5 men can together finish an embroidery work in 4 days, while 3 women & 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, & also that taken by 1 man alone. A person completes work in 2 days Work completed in 1 day = 1/2 A person completes work in 3 days Work completed in 1 day = 1/3 A person completes work in x days Work completed in 1 day = 1/๐ฅ We will use this theory in our question Ex 3.6, 2 Formulate the following problems as a pair of equations, and hence find their solutions: (ii) 2 women & 5 men can together finish an embroidery work in 4 days, while 3 women & 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, & also that taken by 1 man alone. Let time taken by 1 woman to finish the work = x days Work finished by 1 woman in 1 day = 1/๐ฅ Similarly, Let time taken by 1 man to finish the work = y days Work finished by 1 man in 1 day = 1/๐ฆ Given that 2 women and 5 men complete the work in 4 days โด Work finished by 2 women and 5 men in 1 day = 1/4 2 ร (Work finished by 1 woman in 1 day) + 5 ร (Work finished by 1 man in 1 day) 2 ร 1/๐ฅ + 5 ร 1/๐ฆ = 1/4 2/๐ฅ + 5/๐ฆ = 1/4 Also, 3 women and 6 men complete the work in 3 days โด Work finished by 3 women and 6 men in 1 day = 1/3 3 ร (Work finished by 1 woman in 1 day) + 6 ร (Work finished by 1 man in 1 day) 3 ร 1/๐ฅ + 6 ร 1/๐ฆ = 1/3 3/๐ฅ + 6/๐ฆ = 1/3 Our two equations become 2/๐ฅ + 5/๐ฆ = 1/4 โฆ(1) 3/๐ฅ + 6/๐ฆ = 1/3 โฆ(2) So, our equations become 2u + 5v = 1/4 4(2u + 5v) = 1 8u + 20v = 1 3u + 6v = 1/3 3(3u + 6v) = 1 9u + 18v = 1 Hence, our equations are 8u + 20v = 1 โฆ(3) 9u + 18v = 1 โฆ(4) From (3) 8u + 20v = 1 8u = 1 โ 20v u = (1 โ 20๐ฃ)/8 Putting value of u in (4) 9u + 18v = 1 9 ((1 โ 20๐ฃ)/8) + 18v = 1 Multiplying both sides by 8 8 ร 9 ((1 โ 20๐ฃ)/8) + 8 ร 18v = 8 ร 1 9(1 โ 20v) + 144v = 8 9 โ 180v + 144v = 8 โ 180v + 144v = 8 โ 9 โ36v = โ1 v = (โ1)/(โ36) v = 1/36 Putting v = 1/36 in (3) 8u + 20v = 1 8u + 20(1/36) = 1 8u + 5/9 = 1 8u = 1 โ 5/9 8u = (9 โ 5)/9 8u = 4/9 u = 4/(9 ร 8) u = 1/18 Hence, u = ( ๐)/( ๐๐ ), v = ๐/๐๐ But we have to find x & y We know that u = ๐/๐ 1/18 = 1/๐ฅ x = 18 v = ๐/๐ 1/36 = 1/๐ฆ y = 36 So, x = 18 , y = 36 is the solution of the given equation โด Time taken by one woman to finish the work alone = x = 18 days & Time taken by one man to finish the work alone = y = 36 days

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.