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If three numbers a, b, c are in AP with a common difference of 5, and three numbers p, b, q are in GP with a common ratio of 5, also (q - p) is 14.4 times (c - a), find the value of b. Enter -1 if it cannot be determined.
    Correct answer is '30'. Can you explain this answer?
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    If three numbers a, b, c are in AP with a common difference of 5, and ...
    a = b - 5
    c = b + 5
    p = b/5
    q = 5b
    q - p = 14.4 (c - a)
    5b - b/5 = 14.4 (b + 5 - b + 5)
    5b - 0.2b = 14.4 x 10
    4.8b = 144
    b = 30.
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    If three numbers a, b, c are in AP with a common difference of 5, and ...
    Given:
    Three numbers a, b, c are in arithmetic progression (AP) with a common difference of 5.
    Three numbers p, b, q are in geometric progression (GP) with a common ratio of 5.
    (q - p) is 14.4 times (c - a).

    To Find:
    The value of b.

    Solution:

    Step 1: Finding the Values of a, b, c
    Let's assume the three numbers in the AP are a - 5, a, and a + 5.

    Given that the common difference of the AP is 5, we can express the three numbers as:
    a - 5, a, a + 5.

    Step 2: Finding the Values of p, b, q
    Given that the three numbers in the GP are p/5, b, and 5q.

    Given that the common ratio of the GP is 5, we can express the three numbers as:
    p/5, b, 5q.

    Step 3: Finding the Relationship between (q - p) and (c - a)
    We are given that (q - p) is 14.4 times (c - a).

    Substituting the values, we have:
    5q - p = 14.4 * (a + 5 - (a - 5))

    Simplifying the above equation:
    5q - p = 14.4 * 10
    5q - p = 144

    Step 4: Solving the Equations
    We have two equations:
    1. a - 5 + 5 = p/5
    2. 5q - p = 144

    Simplifying equation 1, we get:
    a = p/5 + 5

    Substituting the value of a in equation 2, we get:
    5q - p = 144
    5q - (p/5 + 5) = 144
    5q - p/5 - 25 = 144
    Multiplying the equation by 5 to eliminate the fraction:
    25q - p - 125 = 720
    25q - p = 845

    Now we have two equations:
    1. 5q - p = 144
    2. 25q - p = 845

    Subtracting equation 1 from equation 2:
    25q - p - (5q - p) = 845 - 144
    20q = 701
    q = 701/20 = 35.05

    Substituting the value of q in equation 1:
    5(35.05) - p = 144
    175.25 - p = 144
    -p = 144 - 175.25
    -p = -31.25
    p = 31.25

    Step 5: Finding the Value of b
    From step 2, we know that the three numbers in the GP are p/5, b, and 5q.
    Substituting the values of p and q:
    p/5 = 31.25/5 = 6.25
    5q = 5 * 35.05 = 175.25

    Since b is the common term in the GP, b = 6.25
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    If three numbers a, b, c are in AP with a common difference of 5, and three numbers p, b, q are in GP with a common ratio of 5, also (q - p) is 14.4 times (c - a), find the value of b. Enter -1 if it cannot be determined.Correct answer is '30'. Can you explain this answer?
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    If three numbers a, b, c are in AP with a common difference of 5, and three numbers p, b, q are in GP with a common ratio of 5, also (q - p) is 14.4 times (c - a), find the value of b. Enter -1 if it cannot be determined.Correct answer is '30'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If three numbers a, b, c are in AP with a common difference of 5, and three numbers p, b, q are in GP with a common ratio of 5, also (q - p) is 14.4 times (c - a), find the value of b. Enter -1 if it cannot be determined.Correct answer is '30'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If three numbers a, b, c are in AP with a common difference of 5, and three numbers p, b, q are in GP with a common ratio of 5, also (q - p) is 14.4 times (c - a), find the value of b. Enter -1 if it cannot be determined.Correct answer is '30'. Can you explain this answer?.
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