At a stationery shop it costs ₹ 185 for 4 gel-pens, 8 ball-point pens and one marker pen and ₹ 315 for 7 gel-pens, 15 ball-point pens and one marker pen. Then what would be the cost of one gel-pen, one ball-point pen and one marker pen?

### Concept & Strategy The core strategy here is manipulating a system of linear equations using **linear combination**. Instead of trying to find the individual price of each item (which is impossible since we have 3 variables but only 2 equations), we can multiply the equations by specific factors and add/subtract them to directly arrive at the desired expression: $1g + 1b + 1m$. ### Step-by-Step Solution **Given:** Let the cost of a gel-pen be $g$, a ball-point pen be $b$, and a marker be $m$. 1) $4g + 8b + 1m = 185$ 2) $7g + 15b + 1m = 315$ **Calculation:** We need to find the value of $g + b + m$. Let's look for a multiple of the first equation minus a multiple of the second equation that yields exactly $1g + 1b + 1m$. Notice what happens if we multiply the first equation by 2 and subtract the second equation from it: Step 1: Multiply Eq (1) by 2 $2 \times (4g + 8b + 1m) = 2 \times 185$ $8g + 16b + 2m = 370$ Step 2: Subtract Eq (2) from the new equation $(8g - 7g) + (16b - 15b) + (2m - 1m) = 370 - 315$ $g + b + m = 55$ ### Exam Strategy & Shortcut **Coefficient Matching Pattern:** In bank and competitive exams, whenever you are given 3 variables but only 2 equations, you are almost always expected to find a direct linear combination. Quickly test simple combinations like $2 \times Eq1 - Eq2$ or $3 \times Eq1 - 2 \times Eq2$ on just the first variable. Here, testing $2 \times 4g - 7g = 1g$. Instantly verify if it works for the second variable: $2 \times 8b - 15b = 1b$. It works! You can then immediately calculate $2 \times 185 - 315 = 55$. ### Common Pitfall The most common mistake is wasting precious exam time trying to solve for individual variables ($g$, $b$, or $m$). Students often get stuck realizing there aren't enough equations and end up guessing, not realizing the whole expression can be found at once. ### Final Answer **Therefore, the correct answer is ₹ 55.**