Question

A, B and C are partners sharing in the ratio of 5 : 4 : 3. They admit D for `1/7`th share. It is agreed that B would retain his original share. Sacrificing ratio will be ______.

पर्याय

• A, B and C − 5 : 4 : 3

• A and C − 4 : 3

• A and C − 5 : 4

• A and C − 5 : 3

Answer 1

A, B and C are partners sharing in the ratio of 5 : 4 : 3. They admit D for `1/7`th share. It is agreed that B would retain his original share. Sacrificing ratio will be A and C − 5 : 3.

Explanation:

Calculate the Remaining Share for A and C:

The total share available for A and C is the total profit (1) minus B’s share and D’s share.

Remaining Share = 1 − B’s Share − D’s Share

= `1 - 4/12 - 1/7`

Find a common denominator for 12 and 7, which is 84

Remaining Share = `84/84 - 28/84 - 12/84`

= `44/84`

The remaining `44/84` share is distributed between A and C in their existing 5 : 3 ratio.

A’s New Share = `44/84 xx 5/8`

= `220/672`

C’s New Share = `44/84 xx 3/8`

= `132/672`

A’s Sacrifice = `5/12 - 220/672`

= `(5 xx 56)/(12 xx 56) - 220/672`

= `280/672 - 220/672`

= `60/672`

B’s Sacrifice = B retained his original share, so his sacrifice is 0.

C’s Sacrifice = `3/12 - 132/672`

= `(3 xx 56)/(12 xx 56) - 132/672`

= `168/672 - 132/672`

= `36/672`

Sacrificing ratio of A and C = `60/672 : 36/672` or 60 : 36 or 5 : 3