From a full tank containing 729 liters of honey, we pour off "a" litre

Question

From a full tank containing 729 liters of honey, we pour off "a" litres and add water to fill up the tank. After stirring the solution thoroughly, we pour off "a" liters of the solution and again add water to fill up the tank. After the procedure is repeated for a total of 6 times, the solution contains 64 liters of honey. Find "a"

A) 243 liters
B) 81 liters
C) 2.7 liters
D) 90 liters

A) 243 liters 
B) 81 liters 
C) 2.7 liters 
D) 90 liters

KarishmaB · Accepted Answer

Cfinal = Cf1 *  ^6

64/729 = 1 *  ^6

(\frac{2}{3})^6 =  ^6

\frac{2}{3} = \frac{(729 - a)}{729}

2*243 = 729 - a

a = 243

smitsharma · Answer

Suppose a container contains x units of a liquid from which y units are taken out and replaced by water. After n operations, quantity of pure liquid = 
x(1−y/x)^n (which in this case = 64)

In this case x = 729
y = a
n = 6

By checking option A. Replace a with 243, equate further, and LHS will match RHS viz. 64.

(This is a CAT question, don't worry. You won't encounter such questions on the GMAT)

danlew · Answer

I did not know the formula as well. However, I was able to answer this quite simply by working backwards from answer choices. First, I took choice D, which gives 'a' = 90 litres. Now, if we remove 'a' litres 6 times, we will remove 6*90=540 litres of fluid. Even if we assume 540 litres as entirely honey (which it is not), then the amount of honey remaining after 6 attempts will be 729-540=189 litres However, the question says that amount of honey that should remain is only 64 litres, so going by this, the amount being removed has to be far greater than 90 litres. Conveniently, answer choice A = 243 litres is the only one larger than D, so A is the answer

In case you are wondering, how much honey we will actually remove when we use choice D, here is how to work it: Step 1: From choice D, a = 90, so we remove 90 from 729 = 639 litres of honey remain Step 2: We add a=90 litres of water and remove a=90 litres of mixture. However, this time, only a fraction of the mixture removed is honey, so we need to calculate amount of honey removed. Amount of honey in 90 litres of mixture = 90 * Fraction of money in total mixture = 90* \frac{639}{729} \approx{80} Amount of honey remaining = 639-80 = 559 litres Step 3: We again add a=90 litres of water and remove a=90 litres of mixture Now, the fraction of honey in the 90 litres, will now be even less than 80, so if we were to remove it for 3 more steps, the actual of honey removed will get lower and lower, so no need to even do this calculation.

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From a full tank containing 729 liters of honey, we pour off "a" litre

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