Question

On 1.4.2018, A and B started business with capitals of ₹ 8,00,000 and ₹ 16,00,000 respectively. They decided to share the future profits in the ratio of their capitals. On 1.4.2019, they admitted C as a new partner. A surrendered 1/4th of his share in favour of C and B surrendered 1/9th from his share in favour of C. On 1.4.2020, D was admitted as a new partner for 1/6th share. On 1.4.2021, E was admitted for 1/5 share in the profits and it was decided that all the partners will share the future profits equally.

1. The profit sharing ratio of A, B, and C was ______.
   1. 9 : 20 : 7
   2. 8 : 21 : 7
   3. 10 : 19 : 7
   4. 7 : 22 : 7
2. The profit sharing ratio of A, B, C, and D was ______.
   1. 45 : 105 : 30 : 36
   2. 45 : 100 : 35 : 36
   3. 45 : 105 : 40 : 36
   4. 45 : 100 : 40 : 36

Answer 1

1. The profit sharing ratio of A, B, and C was 9 : 20 : 7.
2. The profit sharing ratio of A, B, C, and D was 45 : 100 : 35 : 36.

Explanation:

1.

Old Share of A and B = 1 : 2

A’s New share = `1/3 xx (1 - 1/4)`

= `1/3 xx 3/4`

= `3/12`

= `(1 xx 9)/(4 xx 9) = 9/36`

B’s New share = `2/3 - 1/9`

= `(2 xx 3)/(3 xx 3) - 1/9`

= `6/9 - 1/9`

= `5/9`

To simplify, use a common denominator of 36:

A’s New share = `3/12`

= `(3 xx 3)/(12 xx 3)`

= `9/36`

B’s New share = `5/9`

= `(5 xx 4)/(9 xx 4)`

= `20/36`

Calculating C’s Share:

In any partnership firm, the Total Share of Profit is always 1 (which is equivalent to `36/36`).

C’s Share = Total Share − (A’s New Share + B’s New Share)

C’s Share = `1 - (9/36 + 20/36)`

= `36/36 - 29/36`

= `7/36` 

A : B : C = `9/36 : 20/36 : 7/36` or 9 : 20 : 7

2.

D’s share = `1/6`

Remaining share = `1 - 1/6 = 6/6 - 1/6 = 5/6`

A’s New share = `9/36 xx 5/6`

= `45/216`

B’s New share = `20/36 xx 5/6`

= `100/216`

C’s New share = `7/36 xx 5/6`

= `35/216`

D’s adjusted share = `1/6`

= `(1 xx 36)/(6 xx 36)`

= `36/216`

A : B : C : D = `45/216 : 100/216 : 35/216 : 36/216` or 45 : 100 : 35 : 36