Maths question from Jr. Assistant exam, 2026 by JKSSB
A barrel contains a mixture of wine and water in the ratio 3:1. How much fraction of the mixture must be drawn off and substituted by water so that the ratio of wine and water in the resultant mixture in the barrel becomes 1:1?
Last updated Jun 24, 2026
Correct Answer:
Option B —
1/3
To solve this, imagine a barrel that holds a total of 4 liters. In the beginning, because the ratio is 3 to 1, you have 3 liters of wine and 1 liter of water.
The Goal
You want the final mixture to be a 1 to 1 ratio. Since the total volume remains the same (4 liters), your goal is to end up with 2 liters of wine and 2 liters of water.
Step-by-Step Logic
Analyze the Wine:
To go from 3 liters of wine down to 2 liters, you need to remove exactly 1 liter of wine.
Determine how much mixture to remove:
You cannot remove wine by itself; you have to draw off the mixture. Since the mixture is 3 parts wine out of 4 total parts, every time you take out a cup of liquid, 3/4 of that cup is wine.
To remove 1 full liter of wine, you need to draw off a total of 1 and 1/3 liters of the mixture.
(Check: 3/4 of 1 and 1/3 equals 1).
Calculate the Fraction:
Now, compare the amount you removed (1 and 1/3 liters) to the total amount in the barrel (4 liters).
1 and 1/3 divided by 4 is the same as 4/3 divided by 4.
This simplifies to 1/3.
Summary
By drawing off one-third of the mixture and replacing that specific amount with pure water, the concentration of wine drops just enough to reach the equal 1 to 1 balance.
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
