Question

Roshi and Riya are partners sharing profits and losses in the ratio of 5 : 3. Maria is admitted into the firm. Roshi sacrifices 1 /5 of her share and Riya sacrifices 1/6 in favour of Maria. Calculate the new ratio.

Answer 1

Old ratio = 5:3

Roshi's sacrifice of share = \(\frac{1}{5}\, of \, \frac{5}{8} = \frac{1}{5} \times \frac{5}{8}\) = \(\frac{5}{40}\)

Roshi's new share = \(\frac{5}{8} - \frac{5}{40} = \frac{25-5}{40} = \frac{20}{40}\)

Riya's sacrifice of share = \(\frac{1}{6} \,of\, \frac{3}{8} = \frac{1}{6} \times \frac{3}{8} = \frac{3}{48}\)

Riya's  new share = \(\frac{3}{8} - \frac{3}{48} = \frac{18-3}{48} = \frac{15}{48}\)

Riya's new share = \(\frac{3}{8} - \frac{3}{48} = \frac{18-3}{48} = \frac{15}{48}\)

Maria's share = \(\frac{5}{40} + \frac{3}{48} = \frac{30+15}{240} = \frac{45}{240}\)

New profit sharing ratio = \(\frac{20}{40} : \frac{6}{68} : \frac{45}{240} = \)\(\frac{120}{240} : \frac{30}{240} : \frac{45} {240}\)

= 120 : 75 : 45 = 8 : 5 : 3