There are five identical cups containing milk in the ratio 4 : 5 : 6 : 7 : 8. How many cups are at least half full of milk if the total volume of milk in the cups is three-fifth of the total volume of the five cups?
Explanation:
Let the quantities of milk in the cups be 4x ml, 5x ml, 6x ml, 7x ml and 8x ml. Let the volume of each cup be 100 ml.
Total volume of the cups = 500 ml
4x + 5x + 6x + 7x + 8x = 0.6 × 500 = 300
⇒ 18x = 300
⇒ x = 100/9
The quantities of milk in the cups are 400/9 ml, 500/9 ml, 600/9 ml, 700/9 ml and 800/9 ml
i.e., except the first cup all other are filled with milk at least to 50% of their capacity.
Hence, 4.
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