A woman distributed her savings among her daughters A, B and C in the ratio 6…

2020

A woman distributed her savings among her daughters A, B and C in the ratio 6 : 7 : 11. If B gives Rs. 700 from her share to A, the ratio of shares of A, B and C becomes 5 : 4 : 3. What is the average of the shares (in Rs.) of A and B in the beginning?

  1. A.

    3722

  2. B.

    4550

  3. C.

    5100

  4. D.

    4750

Attempted by 1 students.

Show answer & explanation

Correct answer: A

CONCEPT: In a ratio-transfer problem, assign one multiplier to the original ratio and write the changed shares after the transfer. The new ratio gives an equation between the changed quantities, which determines the multiplier.

APPLICATION:

  1. Let the original shares of A, B and C be 6x, 7x and 11x.

  2. After B gives Rs. 700 to A, the changed shares of A and B are 6x + 700 and 7x - 700.

  3. From the new ratio A : B = 5 : 4, (7x - 700)/(6x + 700) = 4/5.

  4. Cross-multiplying gives 5(7x - 700) = 4(6x + 700), so 35x - 3500 = 24x + 2800.

  5. Therefore 11x = 6300 and x = 6300/11.

  6. The initial sum of A and B is 6x + 7x = 13x = 81900/11, so their average is (81900/11)/2 = 81900/22 = 3722.72. The exact average is Rs. 3722.72; the listed integer form used in the choices is 3722.

CROSS-CHECK: With x = 6300/11, the changed shares satisfy (6x + 700) : (7x - 700) = 5 : 4, matching the given A : B relation after transfer.

Result: the calculation gives Rs. 3722.72, represented in the choices by 3722.

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