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.

If ratio of their profit shares was 20: 51, then find the difference between profit shares of Avni and Beena,

  1. A.

    Rs.4350

  2. B.

    Rs.5120

  3. C.

    Rs.6200

  4. D.

    Rs.7200

  5. E.

    Rs.6700

Attempted by 1 students.

Show answer & explanation

Correct answer: C

Concept

When a profit is divided between partners in a fixed ratio, write the ratio as a sum of equal parts. The value of one part equals the combined money the partners share divided by the total number of parts. Each partner's money = (their parts) x (value of one part), and the difference between two partners = (difference in their parts) x (value of one part).

Note: the passage also introduces P, 'x' months, Chetna's entry, and a hypothetical 10 : 27 ratio, but this specific question already supplies the operative figures directly (combined profit Rs.14200 and profit-share ratio 20 : 51), so those other variables do not need to be solved for here.

Application

  1. The operative data: Avni and Beena together receive Rs.14200, and their profit shares are in the ratio 20 : 51.

  2. Total number of equal parts = 20 + 51 = 71.

  3. Value of one part = 14200 / 71 = Rs.200.

  4. Avni's share = 20 x 200 = Rs.4000; Beena's share = 51 x 200 = Rs.10200.

  5. Difference = 10200 - 4000 = Rs.6200. A shortcut: difference in parts = 51 - 20 = 31, so difference = 31 x 200 = Rs.6200.

Cross-check

Add the two shares back: 4000 + 10200 = 14200, which matches the given combined amount, and 4000 : 10200 reduces to 20 : 51. Both conditions hold, so the difference Rs.6200 is correct.

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