Ask Question
5 December, 17:51

Three numbers are in the ratio 3:9:10. If 10 is added to the last number, then the three numbers form an arithmetic progression. What are the three numbers?

+2
Answers (1)
  1. 5 December, 20:30
    0
    The numbers are 6, 18, and 30

    Step-by-step explanation:

    If the three numbers are in the ratio of 3:9:10,

    let the numbers be 3x, 9x and 10x.

    If 10 is added to the last number to form an arithmetic progression

    Then, 3x 9x (10x+10) are the progression

    The common difference of an arithmetic progression (d) = T₂ - T₁ = T₃ - T₂

    T₂-T₁ = T₃ - T₂ ... Equation 1

    Where T₁ = first term of the progression, T₂ = Second term of the progression, T₃ = third term of the progression

    Given: T₁ = 3x, T₂ = 9x, T₃ = 10x + 10

    Substituting these values into equation 1

    9x-3x = (10x+10) - 9x

    Solving the equation above,

    3x = 10+x

    3x-x = 10

    2x = 10

    x = 10/2

    x = 2.

    Therefore the numbers are 6, 18, and 30
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “Three numbers are in the ratio 3:9:10. If 10 is added to the last number, then the three numbers form an arithmetic progression. What are ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers