Learn all Concepts of Chapter 3 Class 10 (with VIDEOS). Check - Linear Equations in 2 Variables - Class 10    1. Chapter 3 Class 10 Pair of Linear Equations in Two Variables
2. Serial order wise
3. Ex 3.5

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 and it becomes 1/4 when 8 is added to its denominator. Find the fraction Let numerator be x and denominator be y So, fraction is 𝑥/𝑦 Given that, if 1 is subtracted from numerator fraction becomes 1/3. (𝑁𝑢𝑛𝑒𝑟𝑎𝑡𝑜𝑟 −1)/(𝐷𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟 )=1/3 (𝑥 − 1)/(𝑦 )=1/3 3(x – 1) = 1(y) 3x – 3 = y 3x – y = 3 Also, if 8 is added to the denominator, fraction becomes 1/4. (𝑁𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟 )/(𝐷𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟 + 8)=1/4 (𝑥 )/(𝑦 + 8)=1/4 4(x) = 1(y + 8) 4x = y + 8 4x – y = 8 From (1) 3x – y = 3 3x = y + 3 x = ((𝑦 + 3)/3) Putting value of x in (2) 4x – y – 8 = 0 4 ((𝑦 + 3)/3 ) – y – 8 = 0 Multiplying the equation by 3 3 ×"4 (" (𝑦 + 3)/3 ")"−3×𝑦−3×8=0×8 4(y + 3 ) – 3y – 24 = 0 4y + 12 – 3y – 24 = 0 4y – 3y – 24 + 12 = 0 y – 12 = 0 y = 12 Putting y = 12 in equation (1) 3x – y = 3 3x – 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 Hence, original fraction = 𝑁𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟/𝐷𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟 "= " 𝑥/𝑦=5/12

Ex 3.5 