How to solve

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# Question

# Answer

**Step 1: Write down the draining ratio for both scenarios**

Scenario 1:

X : Y

104 : 34

3 : 1

Scenario 2:

X : Y

34 : 104

1 : 3

**Step 2: Make the ratio of Tank Y the same since it is a constant (completely drained in both scenarios)**

Scenario 1:

X : Y

104 : 34

3 : 1

9 : 3

Scenario 2:

X : Y

34 : 104

1 : 3

**Step 3: Identify that the difference in units for Tank X represents the difference in water left in Tank X for both scenarios**

9 units – 1 unit = (1176 – 420)

8 units = 756

**Step 4: Solve for both Tanks**

1 unit = 94.5

3 units = 94.5 x 3 = 283.5 litres (water in Tank Y at first since it is completely drained)

From scenario 2:

94.5 + 1176 = 1270.5 litres (water in Tank X at first)

**Step 5: Find difference in volume between both tanks**

Difference in water volume:

1270.5 – 283.5 = **987 litres**

X | Y | Left in X (litres) | |

Draining speed a (litres/hour) | 102 | 34 | 420 |

Draining speed b (litres/hour) | 34 | 102 | 1176 |

In speed a, 3Y+420 = X

In speed b, 1/3Y + 1176 = X

Hence, 3Y + 420 = 1/3 Y + 1176

9/3Y – 1/3Y = 1176 – 420

8/3Y = 756

Y = 756 x 3 ÷8

Y = 283.5 litres

X-Y = 3Y +420 – Y

X-Y = 2Y + 420

X-Y = 567 + 420

X-Y = **987 litres**

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