**Solution**

**Case 1:**

Old Ratio of A, B and C = 5: 4: 1

A’s Sacrifice =1/5 to C

C’s Gain = 1/5

Therefore,

A’s New Share = 5/10 -1/5 = 5 – 2/10 = 3/10

B’s Share = 4/10

C’s New Share = 1/10 + 1/5 = 1 + 2/10 = 3/10

**Therefore, New Ratio of A, B and C = 3: 4: 3**

**Case 2:**

Old Ratio of A, B and C = 5: 4: 1

A’s Sacrifice = 1/10 to C

B’s Sacrifice = 1/10 to C C’s gain = 1/5

Therefore,

A’s New Share = 5/10 – 1/10 = 4/10

B’s New Share = 4/10 – 1/10 = 3/10

C’s New Share = 1/10 + 1/5 = 1+2/10 = 3/10

**Therefore, New Ratio of A, B and C = 4: 3: 3**

**Case 3:**

Old Ratio of A, B and C = 5: 4: 1

New Ratio of A, B and C = 1: 1: 1

Sacrificing Ratio = Old Ratio − New Ratio

Gaining Ratio = New Ratio – Old Ratio

Therefore,

A = 5/10 – 1/3 = 15 – 10/30 = 5/30

B = 4/10 – 1/3 = 12 – 10/30 = 2/30

C = 1/10 – 1/3 = 3 – 10/30 = -3/10

**Therefore, A’s sacrifice = 5/30, B’s sacrifice = 2/30 and C’s gain = 3/10**

**Case 4:**

Old Ratio of A, B and C = 5:4:1

A’s sacrifice = 5/10 x 1/10 = 1/20 to C

B’s sacrifice = 4/10 x 1/2 = 4/20 to C

C’s gain = 1/20 x 4/20 = 5/20

Therefore,

A’s New Share = 5/10 – 1/20 = 10 – 1/20 = 9/20

B’s New Share = 4/10 – 4/20 = 8 – 4/20 = 4/20

C’s New Share = 1/10 + 5/20 = 5 + 2/20 = 7/20

**Therefore, New Ratio of A, B and C = 9: 4: 7**