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

Last updated at July 18, 2026 by Teachoo

Question 27 - The sum of two numbers is 18 & sum of reciprocals 9/40 - CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard

part 2 - Question 27 - CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards - Class 10

part 3 - Question 27 - CBSE Class 10 Sample Paper for 2025 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards - Class 10

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Transcript

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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