Question

R and S are partners sharing profits in the ratio of 5 : 3. T was admitted. R surrenders 1/4 of his share and S 2/5 of his share in favour of T. Calculate the sacrificing ratio and the new ratios.

Answer 1

Given old ratio R : S = 5 : 3.

Total parts = 8.

So:

R's old share = `5/8`

S's old share = `3/8`

1. Sacrifice by R

R surrenders `1/4` of his share:

`1/4 xx 5/8 = 5/32`

2. Sacrifice by S

S surrenders `2/5` of his share:

`2/5 xx 3/8 = 3/20`

So the sacrificing ratio is:

`5/32 : 3/20`

LCM of 32 and 20 = 160:

`25/160 : 24/160`

Sacrificing Ratio: 25 : 24

3. New shares

R: `5/8 - 5/32 = (20 - 5)/32 = 15/32`

S: `3/8 - 3/20 = (15 - 6)/40 = 9/40`

T: `5/32 + 3/20 = (25 + 24)/160 = 49/160`

Convert R and S to denominator 160:

`R = 75/160, S = 36/160, T = 49/160`

Therefore:

New Ratio R : S : T = 75 : 36 : 49