A 70 litre mixture of fruit juice and water contains 10% water by volume. How many litres of water must be added to this mixture so that the new mixture contains 12.5% water by volume (assuming the total volume increases accordingly)?

Introduction / Context:This is a classic dilution and percentage-of-mixture problem. The key idea is to track the amount of water already present, then add more water so that the final fraction of water becomes the required percentage. The fruit juice quantity does not change because only water is added.

Given Data / Assumptions:

• Total mixture initially = 70 litres
• Initial water percentage = 10%
• Final water percentage required = 12.5%
• Only water is added (juice amount stays constant)

Concept / Approach:Water amount = percentage * total. After adding x litres water, set (water + x)/(total + x) = desired percentage.

Step-by-Step Solution:

Verification / Alternative check:If x = 2, final water = 9, final total = 72, and 9/72 = 0.125 = 12.5%. Verified.

Why Other Options Are Wrong:

Common Pitfalls:Many learners mistakenly add 2.5% of 70 directly (which would be 1.75) and stop there, forgetting that the denominator (total volume) also increases when water is added. Always use the fraction equation with (70 + x).

Final Answer:2 litres