In a stationery shop, pencils, pens and exercise books are in the ratio 10 : 2 : 3. If there are 120 pencils in stock, how many exercise books are there?

Introduction / Context:
This problem checks understanding of simple ratios and how to scale them to actual quantities. Questions like this are common in aptitude tests and daily life when inventory or resources must be divided proportionally among different categories such as pencils, pens and exercise books in a shop.

Given Data / Assumptions:
• The ratio of pencils : pens : exercise books is 10 : 2 : 3.
• There are 120 pencils in the shop.
• The numbers of pens and exercise books follow the same fixed ratio.
• All items are assumed to be counted as whole pieces and the ratio is fully respected.

Concept / Approach:
When three quantities are in the ratio 10 : 2 : 3, we represent them as 10k, 2k and 3k for some positive constant k. The actual known quantity is used to determine k. Once k is known from the pencil count, we can immediately calculate the corresponding number of exercise books as 3k. This approach is standard whenever we scale a ratio up or down to match a given actual value.

Step-by-Step Solution:
Step 1: Let the number of pencils, pens and exercise books be 10k, 2k and 3k respectively.Step 2: We are told there are 120 pencils, so 10k = 120.Step 3: Solve for k: k = 120 / 10 = 12.Step 4: The number of exercise books is 3k = 3 * 12 = 36.Step 5: Therefore, the shop has 36 exercise books that maintain the given ratio with 120 pencils.

Verification / Alternative check:
Using k = 12, we can compute the full set of quantities: pencils = 10k = 120; pens = 2k = 24; exercise books = 3k = 36. The ratio 120 : 24 : 36 simplifies by dividing each term by 12, producing 10 : 2 : 3, which matches the original ratio. This confirms that the calculated number of exercise books is consistent and correct.

Why Other Options Are Wrong:
Option 26 would give totals 120 : 24 : 26, which simplifies to 60 : 12 : 13 and does not match 10 : 2 : 3.
Option 46 gives 120 : 24 : 46, which also does not reduce to 10 : 2 : 3.
Option 56 gives 120 : 24 : 56, which simplifies to 15 : 3 : 7 and again is different from 10 : 2 : 3. Thus, only 36 fits the required ratio.

Common Pitfalls:
Students sometimes incorrectly divide 120 directly by the third term of the ratio (3) instead of first finding the scale factor k from the matching term, which is 10 in this case. Another mistake is to misinterpret the ratio as percentages instead of fixed proportional parts, leading to wrong arithmetic. Carefully mapping each ratio term to its corresponding variable expression avoids these errors.

Final Answer:
The number of exercise books in the shop is 36.