In a mixture of milk and water, the proportion of water by weight is 75%. If to 60 g of this mixture an additional 15 g of water are added, what will be the new percentage of water in the resulting mixture? (All weights are in grams.)

Introduction:
This is a straightforward percentage and mixture problem involving milk and water. You are given the initial percentage of water in a mixture by weight, then an additional amount of water is added. The goal is to calculate the new percentage of water in the final mixture. This type of question frequently appears in aptitude and bank exams.

Given Data / Assumptions:

• The mixture consists only of milk and water.
• Initially, water makes up 75% of the mixture by weight.
• The initial amount of mixture considered is 60 g.
• An extra 15 g of water is added to the 60 g of mixture.
• We need to find the new percentage of water in the final mixture.

Concept / Approach:
Percentages can be directly converted to actual weights when we know the total amount of mixture. Here, water is 75% of 60 g. Once we know the initial water and milk weights, we can add the 15 g of water, compute the new total weight and the new water weight, and then express water as a percentage of the new total weight using the formula:
percentage of water = (weight of water / total weight of mixture) * 100.

Step-by-Step Solution:
Step 1: Initial total mixture = 60 g. Step 2: Water is 75% of 60 g, so water weight = 0.75 * 60 = 45 g. Step 3: Milk weight initially = 60 - 45 = 15 g. Step 4: Now an additional 15 g of water is added to the mixture. Step 5: New water weight = 45 + 15 = 60 g. Step 6: Milk weight stays the same at 15 g. Step 7: New total mixture weight = 60 g (water) + 15 g (milk) = 75 g. Step 8: New percentage of water = (60 / 75) * 100. Step 9: 60 / 75 = 4 / 5, so water percentage = (4 / 5) * 100 = 80%.

Verification / Alternative check:
You can reason that initially water is 45 g out of 60 g, so there is already a high proportion of water. Adding more pure water increases the water percentage. Since we add 15 g water, the total increases by one quarter (from 60 g to 75 g), but water increases from 45 g to 60 g, which is four fifths of the new total. That gives 80%, confirming our calculation.

Why Other Options Are Wrong:
70% and 75%: These are lower than the original 75% or equal to it, but adding water must increase the water percentage, not decrease or keep it the same.
62% and 65%: These are far below the original percentage and do not match the simple calculation of 60 / 75 * 100.

Common Pitfalls:
A common mistake is to add 15 g to both milk and water or to think of percentage changes directly without recalculating absolute weights. Another error is to forget that the total weight also changes when extra water is added, so you must divide the new water weight by the new total weight to get the correct percentage.

Final Answer:
The new percentage of water in the mixture is 80%.