Directions : Avni and Beena started a business by investing Rs. P and Rs.1.2P…

2021

Directions : Avni and Beena started a business by investing Rs. P and Rs.1.2P respectively. After 'x' months, Avni withdrew her entire amount and Chetna entered into business. After end of 9 months, Beena increased her initial investment by 25%. On completion of one year, share of Avni and Beena in entire profit was Rs.14200. If Beena would have increased her investment after 'x' months, then ratio of share of Avni and Beena in entire profit would have been 10: 27 respectively. Find the value of 'x'.

  1. A.

    4

  2. B.

    6

  3. C.

    8

  4. D.

    5

  5. E.

    9

Attempted by 1 students.

Show answer & explanation

Correct answer: B

Concept

In a partnership, each partner's share of the profit is proportional to their capital-months — the product of the amount invested and the number of months it stays invested. When one partner's contribution is the same across two scenarios, any change in the profit-sharing ratio must come entirely from the other partner's changed capital-months. Setting up the second partner's capital-months as an expression in the unknown time and equating it to the given ratio isolates that unknown.

Application

  1. Let the unit of investment be P. Avni invests P for x months, so Avni's capital-months = Px in every scenario. Beena starts with 1.2P.

  2. In the hypothetical scenario, Beena raises her investment by 25% after x months: she runs 1.2P for x months, then 1.2P × 1.25 = 1.5P for the remaining (12 - x) months.

  3. Beena's capital-months (hypothetical) = 1.2P × x + 1.5P × (12 - x) = 1.2Px + 18P - 1.5Px = 18P - 0.3Px.

  4. The given hypothetical ratio is Avni : Beena = 10 : 27, so Px / (18P - 0.3Px) = 10 / 27.

  5. Cancel P and cross-multiply: 27x = 10(18 - 0.3x) = 180 - 3x, hence 30x = 180, so x = 6.

Cross-check

Put x = 6 back: Beena's hypothetical capital-months = 18P - 0.3P × 6 = 18P - 1.8P = 16.2P, and Avni's = 6P. The ratio 6 : 16.2 = 60 : 162 = 10 : 27, which matches the given condition exactly. (The actual-scenario figure Rs.14200 and Chetna's entry only fix the money value of the combined share; the value of x is pinned by the ratio condition alone.)

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