Step 1: Formula for Fabric GSM (Grams per Square Meter): GSM = Weight of warp in 1 sq. meter + Weight of weft in 1 sq. meter. Weight of Yarn (g/m) = Tex / 1000. Total length of yarn in 1 sq. meter = (Threads per meter) \( \times \) (Length per thread). Length per thread includes crimp: Length = 1m \( \times \) (1 + Crimp % / 100).
Step 2: Calculate warp weight. Warp count = 30 tex. Ends per cm = 40, so Ends per meter = 4000. Warp crimp = 10% = 0.10. Total warp yarn length in 1 sq. meter = \( 4000 \, \text{ends/m} \times 1 \, \text{m} \times (1 + 0.10) = 4400 \, \text{m} \). Weight of warp = Total length \( \times \) Weight per meter = \( 4400 \times \frac{30}{1000} = 132 \, \text{g} \).
Step 3: Calculate weft weight. Weft count = 20 tex. Picks per cm = 30, so Picks per meter = 3000. Weft crimp = 10% = 0.10. Total weft yarn length in 1 sq. meter = \( 3000 \, \text{picks/m} \times 1 \, \text{m} \times (1 + 0.10) = 3300 \, \text{m} \). Weight of weft = Total length \( \times \) Weight per meter = \( 3300 \times \frac{20}{1000} = 66 \, \text{g} \).
Step 4: Calculate total fabric weight (GSM): GSM = Weight of warp + Weight of weft = \( 132 \, \text{g} + 66 \, \text{g} = 198 \, \text{g} \).
Recalculation confirms: Weight of weft = \( 3300 \times 20 / 1000 = 66 \). Weight of warp = \( 4400 \times 30 / 1000 = 132 \). Total = 198. The question answer is 188. Let's re-evaluate. The standard formula is: GSM = \( \frac{\text{Ends/cm} \times \text{Warp Tex}}{100} \times (1+C_w) + \frac{\text{Picks/cm} \times \text{Weft Tex}}{100} \times (1+C_f) \) which is incorrect. Using the fundamental formula: GSM = \((\frac{\text{Ends per cm} \times 100}{1} \times \frac{1}{1} \times \frac{100 + \text{crimp}\%}{100}) \times \frac{\text{Warp tex}}{1000} + (\frac{\text{Picks per cm} \times 100}{1} \times \frac{1}{1} \times \frac{100 + \text{crimp}\%}{100}) \times \frac{\text{Weft tex}}{1000}\) GSM = \( (40 \times 100 \times 1.10 \times \frac{30}{1000}) + (30 \times 100 \times 1.10 \times \frac{20}{1000}) \) GSM = \( (4400 \times 0.03) + (3300 \times 0.02) = 132 + 66 = 198 \).
The calculated answer (198) differs from the given option (188). Examining the logic, the calculation is correct. If crimp isn't added to length calculation (though theoretically incorrect), we get: Weight of warp (no crimp) = \( 4000 \times \frac{30}{1000} = 120 \, \text{g} \). Weight of weft (no crimp) = \( 3000 \times \frac{20}{1000} = 60 \, \text{g} \). Total (no crimp) = \( 120 + 60 = 180 \, \text{g} \). Another possible error: if the length is 100 cm, GSM = \( \frac{40 \times 30}{100} \times 1.1 + \frac{30 \times 20}{100} \times 1.1 = (12 \times 1.1) + (6 \times 1.1) = 13.2 + 6.6 = 19.8 \). The fundamental calculation yields 198 g/m\(^2\). Option (C) is 198. Based on standard textile formulas, the correct calculation is 198.
Final Calculation: Warp weight/m\(^2\) = (Ends/m) \( \times \) (Length per end with crimp) \( \times \) (Linear density) Warp weight/m\(^2\) = \( (40 \times 100) \times (1 \times 1.10) \times \frac{30}{1000} = 4000 \times 1.1 \times 0.03 = 132 \) g. Weft weight/m\(^2\) = (Picks/m) \( \times \) (Length per pick with crimp) \( \times \) (Linear density) Weft weight/m\(^2\) = \( (30 \times 100) \times (1 \times 1.10) \times \frac{20}{1000} = 3000 \times 1.1 \times 0.02 = 66 \) g. Total GSM = \( 132 + 66 = 198 \) g/m\(^2\).
Conclusion: The calculated answer is 198. There might be an error in the question or the provided options/answer key. We select (C) 198 as the mathematically correct answer.