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Example 19 - Present ages of Anu and Raj are in ratio 4:5. Eight years

Example 19 - Chapter 2 Class 8 Linear Equations in One Variable - Part 2

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Question 15 Present ages of Anu and Raj are in the ratio 4 : 5. Eight years from now the ratio of their ages will be 5:6. Find their present ages. Given that, Present ages of Anu and Raj are in the ratio 4 : 5 (π‘ƒπ‘Ÿπ‘’π‘ π‘’π‘›π‘‘ π‘Žπ‘”π‘’ π‘œπ‘“ 𝐴𝑛𝑒)/(π‘ƒπ‘Ÿπ‘’π‘ π‘’π‘›π‘‘ π‘Žπ‘”π‘’ π‘œπ‘“ π‘…π‘Žπ‘—)=4/5 Let present age of Anu = 4x Years & present age of Raj = 5x years After 8 years from now, Anu’s age = (4x + 8) years Raj’s age = (5x + 8) years Given that, Ratio of ages after 8 years is 5:6 (𝐴𝑛𝑒^β€² 𝑠 π‘Žπ‘”π‘’ π‘Žπ‘“π‘‘π‘’π‘Ÿ 8 π‘¦π‘’π‘Žπ‘Ÿπ‘ )/(π‘…π‘Žπ‘—^β€² 𝑠 π‘Žπ‘”π‘’ π‘Žπ‘“π‘‘π‘’π‘Ÿ 8 π‘¦π‘’π‘Žπ‘Ÿπ‘ )=5/6 (4π‘₯ + 8)/(5π‘₯ + 8)=5/6 By cross-multiplication 6 (4π‘₯ + 8) = 5 (5π‘₯ + 8) (6 Γ— 4)π‘₯+ (6 Γ— 8) = (5 Γ— 5)π‘₯ + (5 Γ— 8) 24π‘₯+ 48 = 25π‘₯+ 40 48 βˆ’ 40 = 25π‘₯βˆ’ 24π‘₯ 8 = π‘₯ π‘₯ = 8 ∴ Present age of Anu = 4π‘₯ = 4 Γ— 8 = 32 years & Present age of Raj = 5π‘₯ = 5 Γ— 8 = 40 Years

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.