Rs. 600 are divided among A, B, C so that Rs. 40 more than 2/5 th of A’s…

2026

Rs. 600 are divided among A, B, C so that Rs. 40 more than 2/5 th of A’s share, Rs. 20 more than 2/7 th of B’s share and Rs. 10 more than 9/17 th of C’s may all be equal. What is A’s share (in Rupees)?

  1. A.

    150

  2. B.

    170

  3. C.

    200

  4. D.

    280

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Show answer & explanation

Correct answer: A

Solution

  1. Let the common value be k, so that 2/5·A + 40 = 2/7·B + 20 = 9/17·C + 10 = k.

  2. Express A, B and C in terms of k:

    A = (5/2)·(k − 40), B = (7/2)·(k − 20), C = (17/9)·(k − 10).

  3. Use A + B + C = 600 and solve for k:

    (5/2)(k − 40) + (7/2)(k − 20) + (17/9)(k − 10) = 600.

    Multiply both sides by 18 to clear denominators:

    45(k − 40) + 63(k − 20) + 34(k − 10) = 10800.

    Simplify: 142k − 3400 = 10800 ⇒ 142k = 14200 ⇒ k = 100.

  4. Find A: A = (5/2)·(100 − 40) = (5/2)·60 = 150. Therefore A's share is Rs. 150.

  5. Verification: 2/5·150 + 40 = 100; B = (7/2)·(100 − 20) = 280; C = (17/9)·(100 − 10) = 170. Sum = 150 + 280 + 170 = 600.

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