A tailor has 37.5 metres of cloth. He can cut 8 equal pieces from each metre of cloth. How many pieces can he make from exactly half of the cloth he has?

Introduction / Context:
This is a straightforward application of fractions and unitary method. We are given the total length of cloth and the number of pieces obtainable from one metre. The problem then asks for the number of pieces that can be cut from half of the total cloth. Such questions are standard in aptitude tests involving proportional reasoning.

Given Data / Assumptions:

• Total length of cloth = 37.5 metres.
• From 1 metre of cloth, the tailor can cut 8 equal pieces.
• We are interested in half of the total cloth, that is 37.5 / 2 metres.
• All pieces are of equal size.

Concept / Approach:
First, determine the length of cloth in half the total amount. Next, use the rate of 8 pieces per metre to find the number of pieces from that half length. This is essentially multiplying the number of metres in half by the number of pieces per metre.

Step-by-Step Solution:
Step 1: Compute half of 37.5 metres: 37.5 / 2 = 18.75 metres. Step 2: From 1 metre, the tailor can make 8 pieces. Step 3: From 18.75 metres, total pieces = 18.75 × 8. Step 4: Calculate 18.75 × 8 = (18 × 8) + (0.75 × 8) = 144 + 6 = 150. Step 5: Therefore, the tailor can make 150 pieces from half of the cloth.

Verification / Alternative check:
We can find the total pieces from the full 37.5 metres and then divide by 2. From 37.5 metres, total pieces = 37.5 × 8 = 300. Half of 300 is 150, which matches the earlier result. Thus the answer is consistent.

Why Other Options Are Wrong:
300: This is the number of pieces from the full 37.5 metres, not from half of it.
175 and 200: These are higher than the correct count for 18.75 metres and do not match any logical calculation based on 8 pieces per metre.
250: This corresponds to 31.25 metres of cloth, which is more than half of 37.5 metres, so it is not correct.

Common Pitfalls:
Some learners mistakenly multiply the total 37.5 metres by 8 and then forget to halve the number of pieces. Others miscalculate half of 37.5. Always handle the fraction step carefully and then apply the pieces-per-metre rate.

Final Answer:
The tailor can make 150 pieces from half of the cloth he has.