### Brain Teasers

# How Much Brine is in the Tank?

There is a brine in a storage tank that contains 2.5% sodium chloride (NaCl)in water. When you add another kilogram of NaCl the concentration goes up to 3%.

How much brine was originally in the storage tank?

How much brine was originally in the storage tank?

### Answer

Let there be X kg of NaCl and W kg of water in the original solution.From the first statement,

X / (X + W) = 2.5% = 0.025 ---- (1)

After adding 1 kg of NaCl,

(X + 1) / (X + 1 + W) = 3% = 0.03 ---- (2)

From (1): (X + W) / X = 1 / 0.025 = 40

(1a): W = 39X

From (2): (X + 1) / (X + 1 + 39 X) = 0.03

(2a): X = 4.85 kg

(1b): W = 189.15 kg

X + W = 194 kg (original amount of brine in storage tank)

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