For aiming at a target a person gets one rupee each time when he hits it and loses one rupee when he misses it. If he gets ₹ 30 after aiming at the target one hundred times, then how many times did he miss the target?

### Concept & Strategy This is an algebraic word problem mapping actions to gains and losses. Since the gain and penalty are identical (₹ 1), the problem reduces to a simple system of linear equations involving sum and difference. $$ \text{Hits} + \text{Misses} = \text{Total Attempts} $$ $$ \text{Hits} - \text{Misses} = \text{Net Score} $$ ### Step-by-Step Solution * **Given:** Total aims (attempts) = 100. Gain per hit = +1. Loss per miss = -1. Final amount = ₹ 30. * **Set up equations:** Let $h$ be hits and $m$ be misses. 1. $h + m = 100$ (Total attempts) 2. $1h - 1m = 30$ (Net financial result) * **Solve the system:** Add Equation 1 and Equation 2 together. * $(h + m) + (h - m) = 100 + 30$ * $2h = 130$ * $h = 65$ (Total hits) * **Calculate misses:** Substitute $h$ back into the first equation. * $65 + m = 100$ * $m = 100 - 65 = 35$ ### Exam Strategy & Shortcut Using the "Assumed Total" shortcut: If he hit all 100 times, he would have ₹ 100. He actually has ₹ 30. The difference is ₹ 70. Every miss costs him ₹ 2 (the ₹ 1 he didn't win + the ₹ 1 penalty he pays). Total misses = $\frac{70}{2} = 35$. This mental math takes less than 5 seconds. ### Common Pitfall Solving perfectly for $h$ (Hits = 65) but forgetting what the question actually asked for. The question asks for the number of *misses*, not hits. Always re-read the final sentence of the question before marking your option. ### Final Answer **Therefore, the correct answer is 35.**