New share = Old share + Gain
|
A |
B |
C |
| Old ratio |
\(\frac{3}{15}\) |
\(\frac{5}{15}\) |
\(\frac{7}{15}\) |
A’s gain is 3/5 of 7/15 = 21/75
B’s gain is 2/5 of 7/15 = 14/75
A's New share = \(\cfrac{3}{15} + \cfrac{21}{75} = \cfrac{15+21}{75} = \cfrac{36}{75}\)
B's New share = \(\cfrac{5}{15}\) + \(\cfrac{14}{75}\) = \(\cfrac{25+14}{75}\) = \(\cfrac{39}{75}\)
New ratio between A and B = \(\cfrac{36}{75} : \cfrac{39}{75}\)
= 36 : 39 or 12 : 13
Gaining ratio is the proportion in which they have acquired C’s share of profit, i.e., 3 : 2. This can be checked by working out in the following way.
Gaining ratio = New share – old share
A's gain = \(\cfrac{12}{25}- \cfrac{3}{15} = \cfrac{720-30}{150} = \cfrac{420}{150}\)
B's gain = \(\cfrac{13}{25} - \cfrac{5}{15} - \cfrac{78-50}{150} = \cfrac{28}{150}\)
Gaining ratio of A and B = \(\cfrac{42}{150} : \cfrac{25}{150}\)
or 42 : 28 or 3 : 2
