Each one of A and B has some money. If A gives $90 to B then B will have twice the money left with A. But, if B gives $30 to A then A will have thrice as much as is left with B. How much money does each have?


Answer:

A has $186 and B has $102.

Step by Step Explanation:
  1. Let us assume A and B have $x and $y respectively.
  2. A gives $90 to B and then B will have twice the money left with A.

    Money with A = $ (x90)
    Money with B = $ (y+90)
  3. B gives $ 30 to A and then A will have thrice as much as is left with B.

    Money with A = $ (x + 30)
    Money with B = $ (y - 30) \begin{aligned} \therefore \space & x + 30 = 3(y - 30) \\ \implies & x + 30 = 3y - 90 \\ \implies & x - 3y = -120 && \ldots (2) \end{aligned}
  4. On multiplying (1) by 3 we get \begin{aligned} & 6x - 3y = 810 && \ldots (3)\end{aligned}Now, subtracting (2) from (3), we get \begin{aligned} & 5x = 930 \\ \implies & x = 186 \end{aligned}
  5. Now, substituting x = 186 in (1), we get \begin{aligned} & 2(186) - y = 270 \\ \implies & y = 372 - 270 = 102 \end{aligned}
  6. Hence, A has $ 186 and B has $ 102.

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