Linear pricing with a difference constraint The total cost of 12 pens and 5 pencils is ₹ 111. One pencil costs ₹ 5 less than one pen. What is the total cost of 8 pens and 9 pencils?

Introduction / Context:
Price-mix questions use small linear systems. With the total cost of a combination and a per-item difference between two products, you can solve for individual prices and then compute the requested new combination cost.

Given Data / Assumptions:

• Let p = price of one pen; q = price of one pencil.
• 12p + 5q = 111.
• q = p − 5 (pencil costs ₹ 5 less than pen).
• Find cost of 8 pens and 9 pencils = 8p + 9q.

Concept / Approach:
Substitute q = p − 5 into the total equation to solve for p first. Then find q. Use these to compute the new linear combination 8p + 9q. Keep values exact and in rupees.

Step-by-Step Solution:
12p + 5q = 111 and q = p − 5.Substitute: 12p + 5(p − 5) = 111 ⇒ 12p + 5p − 25 = 111.17p = 136 ⇒ p = 8.Then q = p − 5 = 3.Compute 8p + 9q = 8*8 + 9*3 = 64 + 27 = 91.

Verification / Alternative check:
Validate the given total: 12p + 5q = 12*8 + 5*3 = 96 + 15 = 111, matching the statement. Hence, prices are consistent.

Why Other Options Are Wrong:
₹ 89, ₹ 97, ₹ 78: These come from arithmetic slips (e.g., miscomputing 17p, or miscalculating 8p + 9q after finding p and q).

Common Pitfalls:
Reversing the difference (setting q = p + 5), or plugging into the wrong target expression. Ensure q is ₹ 5 less than p and double-check the final multiplication and addition.

Final Answer:
₹ 91