Volume of vessel A, B and C is 30 liters.
Volume of vessel B and E is 50 liters.
Vessel A,
Let quantity of pure milk in vessel A is ‘a’
Quantity of water in vessel A = (30 – a)
CP of mixture in vessel A = a × 40 = 40a
SP of mixture in vessel A = 30 × 50 = 1500
Profit = (1500 – 40a) / 40a = 50% = 50 / 100
3000 – 80a = 40a
a = 300 / 120
a = 25
Hence, quantity of pure milk in vessel A = 25 liters
Quantity of water in vessel A = 30 – 25 = 5 liters
Vessel B,
Quantity of water in the vessel B = 240% of 5 = 12 liters
Quantity of pure milk in vessel B = 30 – 12 = 18 liters
Vessel D,
Let the quantity of pure milk in vessel D is ‘b’
Quantity of water in vessel D = (50 – b)
CP of mixture in vessel D = b × 40 = 40b
SP of mixtures in vessel D = 50 × 40 = 2000
Profit = (2000 – 40b) / 40b = (300 / 7)% = 300 / 700
(50 - b) / b = 3 / 7
350 – 7b = 3b
350 = 10b
b = 350 / 10
b = 35
Hence, quantity of pure milk in vessel D = b = 35 liters
Quantity of water in vessel D = 50 – 35 = 15 liters
Vessel E,
Let quantity of pure milk in vessel E is ‘c’
Quantity of water in vessel E = (50 - c)
CP of mixture in vessel E = c × 40 = 40c
SP of mixture in vessel A = 50 × 25.2 = 1260
Loss = (40c - 1260) / 40c = 25% = 25 / 100
(c – 31.5) / c = ¼
4c – 126 = c
3c = 126
c = 126 / 3
c = 42
Hence, quantity of pure milk in vessel E = c = 42 liters
Quantity of water in vessel E = 50 – 42 = 8 liters
Vessel C,
Quantity of pure milk in vessel C = (1 / 3) × (18 + 42) = 60 / 3 = 20 liters
Quantity of water in vessel C = 30 – 20 = 10 liters
| Vessel (total quantity) | Milk (in liters) | Water (in liters) | Ratio (Milk : Water) |
|---|
| A (30 L) | 25 | 5 | 5 : 1 |
| B (30 L) | 18 | 12 | 3 : 2 |
| C (30 L) | 20 | 10 | 2 : 1 |
| D (50 L) | 35 | 15 | 7 : 3 |
| E (50 L) | 42 | 8 | 21 : 4 |
Part of milk in vessel A = 5 / 6
Part of milk in vessel D = 7 / 10
Since, he used the same cane once from each vessel that means he mixed mixture from each vessel in the ratio 1 : 1.
Let part of milk in the mixture purchased by customer = a
By the rule allegation:
(5/6) (7/10)
a
1 1
a - (7 / 10) = (5 / 6) - a
2a = (46 / 30)
a = 23 / 30
Amount of pure milk in the mixture purchased by customer = 3 × (23 / 30) = 2.3 liters