Two numbers P and Q are such that, the sum of 2 % of P and Sum of 2 % of Q is…

2024

Two numbers P and Q are such that, the sum of 2 % of P and Sum of 2 % of Q is two-third of the sum of 2 % of P and 6 % of Q. Find the ratio of P and Q.

  1. A.

    2 : 5

  2. B.

    3 : 1

  3. C.

    3 : 9

  4. D.

    3 : 8

Attempted by 10 students.

Show answer & explanation

Correct answer: B

Step-by-Step Solution

To find the ratio of P and Q, we translate the problem statement into an algebraic equation.

  1. Define the equation: The problem states: "The sum of 2% of P and 2% of Q is two-thirds of the sum of 2% of P and 6% of Q." (0.02P + 0.02Q) = (2/3) * (0.02P + 0.06Q)

  2. Simplify and Solve:

    • Multiply both sides by 3 to remove the fraction: 3 * (0.02P + 0.02Q) = 2 * (0.02P + 0.06Q)

    • Distribute the constants: 0.06P + 0.06Q = 0.04P + 0.12Q

    • Group terms with P on one side and terms with Q on the other: 0.06P - 0.04P = 0.12Q - 0.06Q 0.02P = 0.06Q

    • Find the ratio P/Q: P/Q = 0.06 / 0.02 P/Q = 3 / 1

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