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Difficulty: HardCaselets and Paragraph-Based Data

Under a State Skill Development Mission, a total of 4,5004,500 candidates were enrolled across three vocational sectors: IT & Electronics, Healthcare & Allied Sciences, and Textile & Apparel. The IT & Electronics sector accounted for 40%40\% of the total enrolled candidates. The ratio of candidates enrolled in Healthcare & Allied Sciences to those in Textile & Apparel was 7:87 : 8. Upon completion of the training, 65%65\% of the enrolled candidates in IT & Electronics successfully obtained certification. The number of certified candidates in Healthcare & Allied Sciences was equal to 80%80\% of the certified candidates in IT & Electronics. If the total number of certified candidates across all three sectors combined was 2,8982,898, what percentage of the enrolled candidates in the Textile & Apparel sector successfully obtained certification?

Answer: 55 %

Answer

The certification percentage of enrolled candidates in the Textile & Apparel sector is 55%55\%.
To find the certification percentage for the Textile & Apparel sector, first determine the enrollment figures: IT & Electronics has 1,8001,800 candidates (40%40\% of 4,5004,500), leaving 2,7002,700 candidates split in a 7:87 : 8 ratio between Healthcare (1,2601,260) and Textile (1,4401,440). Next, calculate certified candidates: IT & Electronics has 1,1701,170 certified (65%65\% of 1,8001,800), and Healthcare has 936936 certified (80%80\% of 1,1701,170). Subtracting these from the total 2,8982,898 certified candidates leaves 792792 certified candidates in Textile & Apparel. Finally, 7921,440×100%=55%\frac{792}{1,440} \times 100\% = 55\%.

Step-by-Step Solution

1
Calculate the number of candidates enrolled in IT & Electronics
Enrolled in IT & Electronics = 0.40×4,500=1,8000.40 \times 4,500 = 1,800 candidates.
IT & Electronics accounts for 40%40\% of the overall 4,5004,500 candidates.
2
Determine enrollment in Healthcare & Allied Sciences and Textile & Apparel
Remaining candidates = 4,500−1,800=2,7004,500 - 1,800 = 2,700. Enrolled in Healthcare = 715×2,700=1,260\frac{7}{15} \times 2,700 = 1,260. Enrolled in Textile = 815×2,700=1,440\frac{8}{15} \times 2,700 = 1,440.
The remaining 2,7002,700 candidates are distributed between Healthcare and Textile in the ratio 7:87 : 8 (total 1515 parts).
3
Calculate certified candidates in IT & Electronics
Certified in IT & Electronics = 0.65×1,800=1,1700.65 \times 1,800 = 1,170 candidates.
65%65\% of the enrolled IT & Electronics candidates achieved certification.
4
Calculate certified candidates in Healthcare & Allied Sciences
Certified in Healthcare = 0.80×1,170=9360.80 \times 1,170 = 936 candidates.
Healthcare certified candidates equal 80%80\% of certified candidates in IT & Electronics.
5
Determine certified candidates in Textile & Apparel
Certified in Textile = 2,898−(1,170+936)=2,898−2,106=7922,898 - (1,170 + 936) = 2,898 - 2,106 = 792 candidates.
Total certified across all sectors is 2,8982,898.
6
Compute the certification rate for Textile & Apparel
Certification percentage = (7921,440)×100%=55%\left(\frac{792}{1,440}\right) \times 100\% = 55\%.
Divide certified Textile candidates by total enrolled Textile candidates and convert to percentage.

Key Concept

Data extraction, ratio partitioning, and sequential percentage calculation from unstructured text caselets.
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Topics

Caselets and Paragraph-Based Data

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