New Enroll in RBI Grade B New Batch - Starts on May 21

    Question

    Two positive integers multiply to 5070, with their

    highest common factor being 13 and their sum amounting to 143. What is the difference between these two integers?
    A 26 Correct Answer Incorrect Answer
    B 39 Correct Answer Incorrect Answer
    C 52 Correct Answer Incorrect Answer
    D 13 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let the two numbers be ‘13a’ and ‘13b’ ATQ; 13a × 13b = 5070 So, (a × b) = 30 ……………………. (1) Also, 13a + 13b = 143 So, a + b = 11 Or, a = (11 – b) …………………... (2) Putting value of ‘a’ in equation (1), we have (11 – b) × b = 30 Or, 11b – b2 = 30 Or, b2 – 11b + 30 = 0 Or, b2 – 6b – 5b + 30 = 0 Or, b(b – 6) – 5(b – 6) = 0 Or, (b – 6)(b – 5) = 0 So, b = 6 or b = 5 So, the two numbers are = 13 × 5 = 65 and 13 × 6 = 78 Required difference = 78 - 65 = 13 

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