Ex 3.3, 3 (v) - A fraction becomes 9/11, if 2 is added to both numer

Ex 3.3, 3 (v) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 2
Ex 3.3, 3 (v) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 3
Ex 3.3, 3 (v) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 4
Ex 3.3, 3 (v) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 5
Ex 3.3, 3 (v) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 6

 

 

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

Transcript

Ex 3.3, 3 Form the pair of linear equations for the following problems and find their solution by substitution method. (v) A fraction becomes 9/11 , if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 5/6 . Find the fraction. Let Numerator be x & Denominator be y So, fraction is ๐’™/๐’š Given that If 2 is added to both the numerator and the denominator, fraction becomes 9/11 (๐‘ต๐’–๐’Ž๐’†๐’“๐’‚๐’•๐’๐’“ + ๐Ÿ)/(๐‘ซ๐’†๐’๐’๐’Ž๐’Š๐’๐’‚๐’•๐’๐’“ + ๐Ÿ)=๐Ÿ—/๐Ÿ๐Ÿ (๐‘ฅ + 2)/(๐‘ฆ + 2)=9/11 11(x + 2) = 9(y + 2) 11x + 22 = 9y + 18 11x โ€“ 9y = 18 โˆ’ 22 11x โ€“ 9y = โˆ’4 Also, Given that if 3 is added to both the numerator and the denominator, fraction becomes 5/6 (๐‘ต๐’–๐’Ž๐’†๐’“๐’‚๐’•๐’๐’“ + ๐Ÿ‘)/(๐‘ซ๐’†๐’๐’๐’Ž๐’Š๐’๐’‚๐’•๐’๐’“ + ๐Ÿ‘)=๐Ÿ“/๐Ÿ” (๐‘ฅ + 3)/(๐‘ฆ + 3)=5/6 6(x + 3) = 5(y + 3) 6x + 18 = 5y + 15 6x โ€“ 5y = 15 โˆ’ 18 6x โ€“ 5y = โˆ’3 Hence, our equations are 11x โ€“ 9y = โˆ’4 โ€ฆ(1) 6x โ€“ 5y = โˆ’3 โ€ฆ(2) From (1) 11x โ€“ 9y = โˆ’4 11x = 9y โ€“ 4 x = ((๐Ÿ—๐’š โˆ’ ๐Ÿ’)/๐Ÿ๐Ÿ) Putting x in (2) 6x โ€“ 5y + 3 = 0 6 ((9๐‘ฆ โˆ’ 4)/11) โ€“ 5y + 3 = 0 Multiply both sides by 11 11 ร—(6 (9๐‘ฆ โˆ’ 4))/11 โˆ’5๐‘ฆร—11+3ร—11=0ร—11 6(9y โ€“ 4 ) โ€“ 55y + 33 = 0 6(9y) โ€“ 6(4) โ€“ 55y + 33 = 0 54y โ€“ 24 โ€“ 55y + 33 = 0 โ€“y + 9 = 0 y = 9 Putting y = 9 in (1) 11x โ€“ 9y = โˆ’4 11x โ€“ 9(9) = โˆ’4 11x โ€“ 81 = โˆ’4 11x = โˆ’4 + 81 11x = 77 x = 77/11 x = 7 Therefore x = 7, y = 9 So, Numerator = x = 7 Denominator = y = 9 Hence, Original fraction = ๐‘๐‘ข๐‘š๐‘’๐‘Ÿ๐‘Ž๐‘ก๐‘œ๐‘Ÿ/๐ท๐‘’๐‘›๐‘œ๐‘š๐‘–๐‘›๐‘Ž๐‘ก๐‘œ๐‘Ÿ "= " ๐‘ฅ/๐‘ฆ =๐Ÿ•/๐Ÿ—

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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.