Question

A, B and C are partners sharing profits in the ratio of 3 : 2 : 1. They agree to admit D into the firm. A, B and C agreed to give `1/3rd, 1/6th, 1/9th` share of their profit. The share of profit of D will be ______.

Options

• `1/10`

• `11/54`

• `12/54`

• `13/54`

Answer 1

A, B and C are partners sharing profits in the ratio of 3 : 2 : 1. They agree to admit D into the firm. A, B and C agreed to give `1/3rd, 1/6th, 1/9th` share of their profit. The share of profit of D will be `bbunderline(13/54)`.

Explanation:

Old Share of profit = `3/6, 2/6, 1/6`

Sacrificing Ratio = `1/3, 1/6, 1/9`

The amount given up by each partner to D:

A = `1/3 xx 3/6`

= `3/18`

B = `1/6 xx 2/6`

= `2/36`

C = `1/9 xx 1/6`

= `1/54`

Calculate D’s total share of profit:

D’s Share = A’s sacrifice + B’s sacrifice + C’s sacrifice

= `3/18 + 2/36 + 1/54`

= `(3 xx 6)/(18 xx 6) + (2 xx 3)/(36 xx 3) + (1 xx 2)/(54 xx 2)`

= `18/108 + 6/108 + 2/108`

= `(18 + 6 + 2)/108`

= `26/108`

The fraction is divided by the numerator and the denominator by their greatest common divisor, which is 2:

D’s Share = `13/54`