Two pipes A and B each can fill a tank in 20 mins and 30 mins respectively. A carries milk and B carries water. At 12 noon they simultaneously started filling water and milk together but unfortunately a leak in the form of a circular hole occured at 12:06 p.m. The size of the leak is such that it can
evacuate the tank within 20 minutes. At 12:12 the area of the circle doubled. What will be the ratio of milk and water at 12:18, if milkman with impatience suddenly fills up the rest of the tank by water at 12:18? a. 9 : 16 b. 11 : 17 c. Data insufficient d. None of these |
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A fills up = 60/20 = 3 units/min. AND B fills up = 60/30 = 2 units/min.
1. Till 12:06 P.M.
Water Milk Total Left
12 18 30 30
The leak takes 3 units/min.
effectively filling up/min after 12 : 06 p.m.
= 3 + 2 – 3 = 2 units/min.
2. Till 12:12 p.m.
Total units filled up = 30 + 2 × 6 = 42 units
where milk : water = 3 :2
effective filling up after 12:12 p.m per minute
= 3 + 2 – 6 = –1 unit
3. At 12:18 p.m (before water pouring).
Total solution = 42 + 6 × (–1) = 36 units
where Milk : Water = 3 : 2
=> Milk = (3/5)*36 and water = (2/5)*36
24 units still vacant of the tank and that was suddenly filled up by Milkman so at 12 : 18 after water pouring
Milk = 3 * 36 /5
Water = (2*36/5)+ 24= 192/5
∴ Milk : Water = 3 × 36 :192 = 9 : 16.
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