CAT 1994 — QA Question 28
Answer the next 3 questions based on the information given below:
Alphonso, on his death bed, keeps half his property for his wife and divide the rest equally among his three sons Ben, Carl and Dave. Some years later Ben dies leaving half his property to his widow and half to his brothers Carl and Dave together, shared equally. When Carl makes his will he keeps half his property for his widow and the rest he bequeaths to his younger brother Dave. When Dave dies some years later, he keeps half his property for his widow and the remaining for his mother. The mother now has Rs. 1,575,000.
There is a leak in the bottom of the tank. This leak can empty a full tank in 8 hours. When the tank is full, a tap is opened into the tank which admits 6 litres per hour and the tank is now emptied in 12 hours. What is the capacity of the tank?
Answer & solution
- A
28.8 litres
- B
36 litres
144 litres
- D
Cannot be determined
Since the leak can empty the tank in 8 hours, the rate of leak = .
And since the leak along with the tap can empty it in 12 hours, the equation can be rewritten as:
(where x is the time taken by the tap to fill the tank).
Simplifying we get, or x = 24.
This means that the tap can fill the tank in 24 hours.
Since the tap admits 6 litres per hour, it will admit (6 × 24) = 144 litres in 24 hours, which should be the capacity of the tank