A house owner is told that painting his house will require 45 kg of paint allowing for 6 percent wastage. If paint is available only in 4 kg tins, how many tins are required for painting the house?

Introduction / Context:
This problem is about adjusting a required quantity for wastage and then translating that adjusted requirement into discrete package sizes. Painters often allow for a percentage of wastage when estimating materials. The question checks whether you can handle percentage increase and then compute how many whole tins must be purchased to satisfy that requirement, since fractional tins cannot be bought.

Given Data / Assumptions:

• Net paint required for actual painting work is 45 kg, allowing for 6 percent wastage.
• This statement means that after wastage, 45 kg remains available for application.
• Paint is sold only in tins of 4 kg each.
• We must buy enough tins so that the usable paint after wastage is at least 45 kg.

Concept / Approach:
If 6 percent of the paint will be wasted, then only 94 percent (100 percent minus 6 percent) of the purchased paint will actually be used. Let the total purchased paint be P kg. Then 94 percent of P must equal 45 kg. From this equation we solve for P, then divide by 4 to find how many 4 kg tins are required. Since we cannot buy a fraction of a tin, we round up to the next whole number.

Step-by-Step Solution:
Step 1: Let total paint purchased be P kg.Step 2: Wastage is 6 percent, so usable paint is 94 percent of P, which is 0.94P.Step 3: According to the problem, the usable paint must be 45 kg, so 0.94P = 45.Step 4: Solve for P: P = 45 / 0.94.Step 5: Numerically, 45 / 0.94 is approximately 47.872 kg.Step 6: Paint tins are 4 kg each, so number of tins required = P / 4 ≈ 47.872 / 4 ≈ 11.968.Step 7: Since we cannot buy a fraction of a tin, we must buy 12 tins to meet the requirement.

Verification / Alternative check:
Check with 12 tins. Twelve tins provide 12 * 4 = 48 kg of paint. Wastage is 6 percent of 48 kg, which is 0.06 * 48 = 2.88 kg. The usable paint is 48 - 2.88 = 45.12 kg, which is slightly more than the required 45 kg. With 11 tins, total paint would be 44 kg, and even with zero wastage this would be less than 45 kg. Therefore 12 tins are the minimum that satisfy the requirement with wastage.

Why Other Options Are Wrong:
Eleven tins give only 44 kg of paint, which even without wastage is insufficient. Ten tins provide 40 kg, which is even further from the requirement. Thirteen or fourteen tins provide more paint than necessary and would cover the requirement but are not the least number needed. The question asks for the number of tins required, which implies the smallest integer that meets the need, so 12 is correct.

Common Pitfalls:
Some students misinterpret the phrase allowing 6 percent wasting and assume that 45 kg already includes wastage, leading them to calculate 94 percent of 45 instead of the other way around. Others may forget to round up the number of tins and instead choose 11 based on the approximate division result. In real situations, insufficient paint would be a problem, so always round up when dealing with package counts.

Final Answer:
The house owner must purchase 12 tins of paint, so the correct option is 12.