Transfer Ratio

1. 1Tank A share of the totalThe initial 3:1 ratio makes 4 equal units. Tank A has 3 of them, or 3/4 of the total.A_init = 3/4 × Total
2. 2Mark 10 L transferMoving 10 L from A lowers A and raises B by the same amount. The combined amount stays the same.Transfer = 10 L
3. 3Transfer and regroupAfter moving 10 L, regroup the bars to show the new ratio 2:1.A_after = 2/3 × Total
4. 4Compare the new sharesThe new 2:1 ratio makes 3 equal units. Tank A now represents 2/3 of the total.A_after = 2/3 × Total
5. 5Find the transferred fractionTank A loses the difference between its initial and final shares. That difference is the fraction transferred.3/4 − 2/3 = 1/12
6. 6Calculate the total oilDivide the known transfer amount by the fraction of the total that was transferred.Total = 10 ÷ 1/12 = 120 L
7. 7Find the initial amountsUse the initial ratio and the total to find the amount that was in each tank.A = 3/4 × 120 = 90 L; B = 1/4 × 120 = 30 L
8. 8Check the AnswerTest both givens: the initial amounts must add up to the total of 120 L, and after moving 10 L the tanks must match the ratio 2:1.90 + 30 = 120 L ✓ · 80 : 40 = 2 : 1 ✓

Change the numbers to test the engine with any sum & difference problem: