Question

Calculate sacrificing ratios in the following cases:

1. X and Y are sharing profits in the ratio of 4 : 3. Z joins and the new ratios are 7 : 4 : 3.
2. X and Y are sharing profits in the ratio of 7 : 5. Z joins and the new ratios are 13 : 7 : 4.
3. A and B are sharing profits in the ratio of 5 : 3. C joins and the new ratios are 4 : 2 : 1.
4. A and B are sharing profits in the ratio of 3 : 2. C joins and the new ratios are 5 : 3 : 2.

Answer 1

Sacrificing Share = Old Share − New Share

i. X’s sacrifice = `4/7 - 7/14`

= `(4 xx 2)/(7 xx 2) - 7/14`

= `8/14 - 7/14`

= `1/14`

Y’s sacrifice = `3/7 - 4/14`

= `(3 xx 2)/(7 xx 2) - 4/14`

= `6/14 - 4/14`

= `2/14`

Sacrificing Ratio of X and Y = `1/14 : 2/14` or 1 : 2

ii. X’s sacrifice = `7/12 - 13/24`

= `(7 xx 2)/(12 xx 2) - 13/24`

= `14/24 - 13/24`

= `1/24`

Y’s sacrifice = `5/12 - 7/24`

= `(5 xx 2)/(12 xx 2) - 7/24`

= `10/24 - 7/24`

= `3/24`

Sacrificing Ratio of X and Y = `1/24 : 3/24` or 1 : 3

iii. A’s sacrifice = `5/8 - 4/7`

= `(5 xx 7)/(8 xx 7) - (4 xx 8)/(7 xx 8)`

= `35/56 - 32/56`

= `3/56`

B’s sacrifice = `3/8 - 2/7`

= `(3 xx 7)/(8 xx 7) - (2 xx 8)/(7 xx 8)`

= `21/56 - 16/56`

= `5/56`

Sacrificing Ratio of A and B = `3/56 : 5/56` or 3 : 5

iv. A’s sacrifice = `3/5 - 5/10`

= `(3 xx 2)/(5 xx 2) - 5/10`

= `6/10 - 5/10`

= `1/10`

B’s sacrifice = `2/5 - 3/10`

= `(2 xx 2)/(5 xx 2) - 3/10`

= `4/10 - 3/10`

= `1/10`

Sacrificing Ratio of A and B = `1/10 : 1/10` or 1 : 1