A person has a monthly expenditure of Rs 6000. The expenditure is distributed as follows: Food Rs 2000, Clothing Rs 660, Fuel and rent Rs 1200, Education Rs 480 and Miscellaneous Rs 1660. If these data are represented by a percentage bar diagram of total height 15 cm, what are the lengths, in centimetres, of the two segments of the bar corresponding to education and miscellaneous expenditure respectively?

Introduction / Context:
This problem comes from data interpretation and the concept of percentage bar diagrams. A percentage bar diagram represents the entire quantity as 100 percent and divides a bar of fixed length into segments proportional to the percentages of different components. Here, we convert rupee amounts into percentages of total expenditure and then into segment lengths on a bar of specified height.

Given Data / Assumptions:

Total monthly expenditure = Rs 6000.
Education expenditure = Rs 480.
Miscellaneous expenditure = Rs 1660.
The bar in the percentage diagram has a fixed height of 15 cm representing 100 percent of the expenditure.
We need the lengths of the segments for education and miscellaneous in centimetres.

Concept / Approach:
First, express each category as a percentage of the total. Percentage for a category is (category amount / total amount) * 100. Because 15 cm corresponds to 100 percent in the bar diagram, 1 percent corresponds to 15 / 100 cm = 0.15 cm. Therefore, the length of the segment for any category is its percentage multiplied by 0.15. We apply this to education and miscellaneous expenditures to obtain the required segment lengths.

Step-by-Step Solution:
Total expenditure = 6000. Education percentage = (480 / 6000) * 100. Compute: 480 / 6000 = 0.08, so education = 8 percent. Miscellaneous percentage = (1660 / 6000) * 100. Compute: 1660 / 6000 = 0.276666..., so miscellaneous ≈ 27.666... percent. In the percentage bar diagram, 100 percent corresponds to 15 cm, therefore 1 percent = 15 / 100 = 0.15 cm. Length for education segment = 8 * 0.15 = 1.2 cm. Length for miscellaneous segment = 27.666... * 0.15 = approximately 4.15 cm. Hence, the two required lengths are 1.2 cm for education and 4.15 cm for miscellaneous expenditure.

Verification / Alternative check:
We can verify by checking that percentages sum correctly. Total of all categories is 2000 + 660 + 1200 + 480 + 1660 = 6000, matching the total expenditure. As a further check, we can convert all categories into segment lengths and confirm that they add up to 15 cm. Because each percentage is multiplied by 0.15, the sum of all segment lengths equals 100 * 0.15 = 15 cm, confirming consistency. The pair 1.2 cm and 4.15 cm is therefore correct.

Why Other Options Are Wrong:
1.25 cm and 5 cm correspond to different percentages and would imply education and miscellaneous shares that do not match the given rupee amounts.
1.2 cm and 3.5 cm underestimates the miscellaneous segment and fails to reflect its true proportion of total expenditure.
4.15 cm and 6 cm reverses the relative scale and suggests incorrect segment sizes that do not sum properly with the other categories.
1.5 cm and 4.5 cm come from approximate or rounded percentages rather than the exact ratios and do not align with the precise calculation required in an aptitude test.

Common Pitfalls:
A frequent error is to directly treat rupee amounts as centimetres without converting to percentages, which defeats the idea of a percentage bar. Another mistake is to miscalculate the percentages, for example by dividing incorrectly or rounding too early. Some learners also forget to scale according to the total bar height and use 1 cm as 1 percent instead of the given 15 cm for 100 percent. Always compute the per percent length and then multiply by the correct percentage.

Final Answer:
The lengths of the segments corresponding to education and miscellaneous expenditures are 1.2 cm and 4.15 cm respectively.