An empty vessel was first filled with alcohol. When the vessel got 1/4th empty, it was filled with spirit. Again, when the vessel got 1/3rd… — Answer & Discussion

An empty vessel was first filled with alcohol. When the vessel got 1/4^th empty, it was filled with spirit. Again, when the vessel got 1/3^rd empty, it was filled with alcohol. Again when the vessel got 1/5^th empty, it was filled with spirit. Find the percentage of spirit in the vessel.

A66.66%
B25%
C33.33%
D30%

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Discussion 1

CCommunity29 Apr 2019

Suppose the capacity of vessel is 120 litres and alcohol is filled in it?

When the vessel got 1/4th empty, it was filled with spirit;

∴ Quantity of alcohol = 120 × 3/4 = 90 litres

⇒ Quantity of spirit = 120 × 1/4 = 30 litres

Again when the vessel got 1/3rd empty, it was filled with alcohol;

∴ Quantity of alcohol = 90 × 2/3 + (120/3) = 60 + 40 = 100 litres

Quantity of spirit = 30 × 2/3 = 20 litres

Again, when the vessel got 1/5th empty, it was filled with spirit;

∴ Quantity of alcohol = 100 × 4/5 = 80 litres

Quantity of spirit = 20 × 4/5 + (120/5) = 16 + 24 = 40 litres

∴ Percentage of spirit in the vessel = [40/120] × 100 = 33.33%