Ex 3.5, 4 (ii) - A fraction becomes  1/3  when 1 is subtracted from

Ex 3.5, 4 (ii) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 2
Ex 3.5, 4 (ii) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 3 Ex 3.5, 4 (ii) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 4 Ex 3.5, 4 (ii) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 5

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

Transcript

Ex 3.5, 4 Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method : (ii) A fraction becomes 1/3 when 1 is subtracted from the numerator & it becomes 1/4 when 8 is added to its denominator. Find the fraction Let Numerator be x & Denominator be y So, Fraction is ๐’™/๐’š Given that, If 1 is subtracted from numerator fraction becomes 1/3. (๐‘๐‘ข๐‘š๐‘’๐‘Ÿ๐‘Ž๐‘ก๐‘œ๐‘Ÿ โˆ’ 1)/(๐ท๐‘’๐‘›๐‘œ๐‘š๐‘–๐‘›๐‘Ž๐‘ก๐‘œ๐‘Ÿ )=1/3 (๐‘ฅ โˆ’ 1)/(๐‘ฆ )=1/3 3(x โ€“ 1) = y 3x โ€“ 3 = y 3x โ€“ y = 3 Also, If 8 is added to the denominator, fraction becomes 1/4. (๐‘๐‘ข๐‘š๐‘’๐‘Ÿ๐‘Ž๐‘ก๐‘œ๐‘Ÿ )/(๐ท๐‘’๐‘›๐‘œ๐‘š๐‘–๐‘›๐‘Ž๐‘ก๐‘œ๐‘Ÿ + 8)=1/4 (๐‘ฅ )/(๐‘ฆ + 8)=1/4 4x = y + 8 4x โ€“ y = 8 From (1) 3x โ€“ y = 3 3x = y + 3 x = ((๐’š + ๐Ÿ‘)/๐Ÿ‘) Putting value of x in (2) 4x โ€“ y โ€“ 8 = 0 4 ((๐‘ฆ + 3)/3) โ€“ y โ€“ 8 = 0 Multiplying both sides by 3 3 ร— "4" ((๐‘ฆ + 3)/3)โˆ’"3 ร— " ๐‘ฆโˆ’"3 ร— 8"="3 ร—" 0 4(y + 3 ) โ€“ 3y โ€“ 24 = 0 4y + 12 โ€“ 3y โ€“ 24 = 0 y โ€“ 12 = 0 y = 12 Putting y = 12 in equation (1) 3x โ€“ y = 3 3x โ€“ 12 = 3 3x = 12 + 3 3x = 15 x = 15/3 x = 5 Therefore x = 5, y = 12 is the solution So, Numerator = x = 5 Denominator = y = 12 โˆด 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’™/๐’š=๐Ÿ“/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.