Ratio Split With a Late Adjustment
Three partners agree to split a project surplus of 27,600 in the ratio 5 : 4 : 3. Before payment, a 2,400 correction is added to the surplus because an expense was double-counted. The partners decide the correction should be shared in the same ratio rather than going to one partner. One partner claims his share of the original 27,600 should be 11,500 because "5 out of 12 is nearly half." A second partner wants the correction split equally among the three instead. The bookkeeper must produce the final payout per partner and settle both claims with numbers.
1. Compute each partner's final payout under the agreed same-ratio split.
Read the worked answer
Total to distribute = 27,600 + 2,400 = 30,000. Ratio parts = 5 + 4 + 3 = 12.
Value per part = 30,000 / 12 = 2,500.
Payouts: 5 × 2,500 = 12,500; 4 × 2,500 = 10,000; 3 × 2,500 = 7,500. Sum = 30,000. Correct.
2. Evaluate the first partner's claim of 11,500 on the original 27,600.
Read the worked answer
On the original 27,600, value per part = 27,600 / 12 = 2,300.
First partner's share = 5 × 2,300 = 11,500.
So the figure of 11,500 is correct for the original sum only. But it is not his final payout; after the correction his share is 12,500. The claim is arithmetically right but answers the wrong question - a common trap where a correct intermediate is mistaken for the final answer.
3. Quantify what the second partner would gain or lose if the 2,400 correction were split equally instead of by ratio.
Read the worked answer
Equal split: 2,400 / 3 = 800 each.
Ratio split of the correction: value per part = 2,400 / 12 = 200, so shares are 1,000, 800, 600.
Partner 1: equal gives 800 vs ratio 1,000 → loses 200. Partner 2: equal gives 800 vs ratio 800 → unchanged. Partner 3: equal gives 800 vs ratio 600 → gains 200.
So the equal-split proposal shifts 200 from Partner 1 to Partner 3. Partner 2, who proposed it, is exactly indifferent - which is likely why the proposal was made, but it is not neutral overall.