A man has one-rupee, 5-rupee and 10-rupee currency notes of worth ₹ 480. If the number of notes of each denomination be same, then the total number of notes will be

### Concept & Logic When a collection has an equal number of different denominations, we can group one of each denomination together to form a "set". The total value is then a multiple of the value of this single set. ### Step-by-Step Solution * **Given:** Denominations are ₹ 1, ₹ 5, and ₹ 10. The total value is ₹ 480. The number of notes for each denomination is identical. * **Calculation:** Let the number of notes of each individual denomination be $x$. * The value contributed by the ₹ 1 notes is $1x$. * The value contributed by the ₹ 5 notes is $5x$. * The value contributed by the ₹ 10 notes is $10x$. * The sum of these values equals the total amount: $$1x + 5x + 10x = 480$$ $$16x = 480$$ $$x = \frac{480}{16} = 30$$ * The value $x = 30$ represents the number of notes for ONE specific denomination. * The question asks for the **total** number of notes across all three denominations: $$\text{Total notes} = 3 \times x = 3 \times 30 = 90$$ ### Exam Strategy & Shortcut Think of a "bundle" containing exactly one note of each type. The value of one bundle = $₹ 1 + ₹ 5 + ₹ 10 = ₹ 16$. Total money is ₹ 480. Number of bundles = $480 / 16 = 30$ bundles. Since each bundle contains 3 notes, total notes = $30 \times 3 = 90$. ### Common Pitfall The most frequent mistake is solving for $x = 30$ and immediately looking for 30 in the options (or accidentally selecting an adjacent option). You must remember to multiply by the number of different denominations (3) to find the *total* notes. ### Final Answer **Therefore, the correct answer is 90.**