Learn all Concepts of Chapter 3 Class 10 (with VIDEOS). Check - Linear Equations in 2 Variables - Class 10

 

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  1. Chapter 3 Class 10 Pair of Linear Equations in Two Variables
  2. Serial order wise

Transcript

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 = 1/๐‘ฅ 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 = 1/๐‘ฅ Similarly, Let time taken by 1 man to finish the work = y days Work finished by 1 man in 1 day = 1/๐‘ฆ Given that 2 women and 5 men complete the work in 4 days โˆด 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— 1/๐‘ฅ + 5 ร— 1/๐‘ฆ = 1/4 2/๐‘ฅ + 5/๐‘ฆ = 1/4 Also, 3 women and 6 men complete the work in 3 days โˆด 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— 1/๐‘ฅ + 6 ร— 1/๐‘ฆ = 1/3 3/๐‘ฅ + 6/๐‘ฆ = 1/3 Our two equations become 2/๐‘ฅ + 5/๐‘ฆ = 1/4 โ€ฆ(1) 3/๐‘ฅ + 6/๐‘ฆ = 1/3 โ€ฆ(2) Let ๐Ÿ/๐’™ = u & ๐Ÿ/๐’š = v 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 โ€ฆ(3) 9u + 18v = 1 From (3) 8u + 20v = 1 8u = 1 โ€“ 20v u = (1 โˆ’ 20๐‘ฃ)/8 Putting value of u in (4) 9u + 18v = 1 9 ((1 โˆ’ 20๐‘ฃ)/8) + 18v = 1 Multiplying both sides by 8 8 ร— 9 ((1 โˆ’ 20๐‘ฃ)/8) + 8 ร— 18v = 8 ร— 1 9(1 โ€“ 20v) + 144v = 8 9 โ€“ 180v + 144v = 8 โ€“ 180v + 144v = 8 โ€“ 9 โˆ’36v = โ€“1 v = (โˆ’1)/(โˆ’36) 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 โˆ’ 5)/9 8u = 4/9 u = 4/(9 ร— 8) u = 1/18 Hence, u = ( ๐Ÿ)/( ๐Ÿ๐Ÿ– ), v = ๐Ÿ/๐Ÿ‘๐Ÿ” But we have to find x & y We know that u = ๐Ÿ/๐’™ 1/18 = 1/๐‘ฅ x = 18 v = ๐Ÿ/๐’š 1/36 = 1/๐‘ฆ y = 36 So, x = 18 , y = 36 is the solution of the given equation โˆด 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 9 years. He provides courses for Maths and Science at Teachoo.