Question

Bob Marley takes out 8 litres of mango shake from a vessel full of it and then refilled it with water. He repeat the process three more times. The ratio of the quantity of mango shake now left in vessel to that of the initial quantity is 16 ∶ 81. How much mango shake the vessel hold originally?
1. 18 L
2. 42 L
3. 32 L
4. 24 L

Answer 1

Correct Answer - Option 4 : 24 L

Given∶ 

Quantity of mango shake taken out = 8 L

Final ratio of mango shake to that of the initial quantity = 16 ∶ 81

Formula Used∶

 

Suppose  containers contains x of liquid from which y unit are taken out and replaced by water.

After n operations, the quantity of pure liquid = [x (1 - y/x)ⁿ] units.

Calculation∶

Number of operations, n = 4

Let the total quantity of shake originally be x.

The quantity of shake taken out, y = 8 L

So, Quantity of shake left in vessel after 4 operations = [x (1 - y/x)ⁿ] litre

[x (1 - 8/x)⁴] / x = 16/81

⇒ (1 - 8/x)⁴ = (2/3)⁴

⇒ 1 - 8/x = 2/3

⇒ 8/x = 1/3

⇒ x = 24 L

∴The correct option is (4).