Linear scaling of a mixed basket (pens and pencils): The cost of 5 pens and 8 pencils is ₹31 at fixed unit prices. What is the cost of 15 pens and 24 pencils at the same rates?

Introduction / Context:Here, the target basket (15 pens, 24 pencils) is exactly 3 times the original basket (5 pens, 8 pencils). With constant unit prices, the total cost scales by the same factor.

Given Data / Assumptions:

• Cost(5 pens + 8 pencils) = ₹31
• Target: 15 pens + 24 pencils = 3 * (5 pens + 8 pencils)
• Unit prices are constant.

Concept / Approach:Apply linear scaling: multiply the original cost by 3.

Step-by-Step Solution:Cost(target) = 3 * ₹31 = ₹93

Verification / Alternative check:Let pen be p and pencil be q. Then 5p + 8q = 31. The target cost is 3*(5p + 8q) = 93.

Why Other Options Are Wrong:₹99 and ₹96 are not integral multiples of ₹31; “Cannot be determined” is incorrect because the scaling is exact; ₹90 is also not 3 times ₹31.

Common Pitfalls:Trying to compute p and q separately, which is unnecessary when the target is a simple multiple.

Final Answer:₹93