Question 27 - CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at Dec. 13, 2024 by Teachoo

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Question 27 The sum of two numbers is 18 and the sum of their reciprocals is 9/40. Find the numbersLet first number be x Since sum of two numbers is 18 First number + Second number = 18 x + Second number = 18 Second number = 18 − x Now, Sum of reciprocals = 9/40 𝟏/𝒙+𝟏/(𝟏𝟖−𝒙)=𝟗/𝟒𝟎 ((18 − 𝑥) + 𝑥 )/(𝑥(18 − 𝑥))=9/40 (18 )/(𝑥(18 − 𝑥))=9/40 (18 )/9 × 40=𝑥(18 − 𝑥) 2 × 40 = 18x − x2 80 = 18x − x2 x2 − 18x + 80 = 0 We factorize using splitting the middle term method x2 − 10x − 8x + 80 = 0 x(x − 10) − 8(x − 10) = 0 (x − 10) (x − 8) = 0 So, x = 10, 8 Splitting the middle term method We need to find two numbers whose Sum = –18 Product = 80 × 1 = 80 When x = 10 First number = 10 Second number = 18 − 10 = 8 When x = 8 First number = 8 Second number = 18 − 8 = 12 So, two numbers are 8 and 10

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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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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