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The following table shows the percentage (%) distribution of teachers in six different universities A-F. Total number of teachers in university E is 1856. Based on the data in the table, answer the questions.

University-wise Distribution of Teachers

University  Distribution (%) of Teachers 
A 11%
B 17%
C 19%
D 6%
E 29%
F 18%

What is the average number of teachers in Universities A, C, D and F together?

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UGC NET Official Paper-I (Held On: 05 Mar, 2023 Shift 2)
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  1. 854
  2. 3456
  3. 864
  4. 874

Answer (Detailed Solution Below)

Option 3 : 864
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Detailed Solution

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Calculation:
Let total no. of teachers = X

Total Teacher in E university = 29% of X

1856 = 29/100 × X

X = 6400

So, Total number of teachers = 6400

Total number of teachers = 6400

​Percentage of teachers in university A = 11%

∴ Number of teachers in university A = (11/100) × 6400 = 704

Percentage of teachers in university C = 19%

∴ Number of teachers in university C = (19/100) × 6400 = 1216

Percentage of teachers in university D = 6%

∴ Number of teachers in university D = (6/100) × 6400 = 384

Percentage of teachers in university F = 18%

∴ Number of teachers in university F = (18/100) × 6400 = 1152

∴ Total number of teachers in university A, C, D and F = 704 + 1216 + 384 + 1152 = 3456

⇒ Average number of teachers per university = 3456/4 = 864

∴ Average number of teachers = 864

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