Bunuel wrote:
A water tank has inlets of two types A and B. All inlets of type A when open, bring in water at the same rate. All inlets of type B, when open, bring in water at the same rate. The empty tank is completely filled in 30 minutes if 10 inlets of type A and 45 inlets of type B are open, and in 1 hour if 8 inlets of type A and 18 inlets of type B are open. In how many minutes will the empty tank get completely filled if 7 inlets of type A and 27 inlets of type B are open?
A. 40
B. 42
C. 44
D. 46
E. 48
Are You Up For the Challenge: 700 Level QuestionsGiven:
1. A water tank has inlets of two types A and B.
2. All inlets of type A when open, bring in water at the same rate.
3. All inlets of type B, when open, bring in water at the same rate.
4. The empty tank is completely filled in 30 minutes if 10 inlets of type A and 45 inlets of type B are open, and in 1 hour if 8 inlets of type A and 18 inlets of type B are open.
Asked: In how many minutes will the empty tank get completely filled if 7 inlets of type A and 27 inlets of type B are open?
Let inlets A & B fill the water tank in x hours and y hours respectively
The empty tank is completely filled in 30 minutes if 10 inlets of type A and 45 inlets of type B are open
10/(2x) + 45/(2y) = 1
5/x + 45/2y = 1
The empty tank is completely filled in 1 hour if 8 inlets of type A and 18 inlets of type B are open.
8/x + 18/y = 1
5/x + 45/2y = 8/x + 18/y
3/x = 9/2y
6y = 9x
2y = 3x
y = 1.5x
8/x + 18/1.5x = 1
20/x = 1
x = 20
y = 30
In minutes will the empty tank get completely filled if 7 inlets of type A and 27 inlets of type B are open
7/20 + 27/30 = 7/20 + 9/10 = 25/20 = 5/4
Time needed = 4/5 hours = 48 minutes
IMO E
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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com