400 students took a mock test: 60% of the boys and 80% of the girls cleared the cut off in the test. If the total percentage of students clearing the cut off in the test is 65%, then how many girls appeared in the test?  

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UGC NET Paper 1: Held on 14th Oct 2022 Shift 1
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  1. 100
  2. 120
  3. 150
  4. 300

Answer (Detailed Solution Below)

Option 1 : 100
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UGC NET Paper 1: Held on 21st August 2024 Shift 1
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Detailed Solution

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Given:

400 students took a mock test: 60% of the boys

and 80% of the girls cleared the cut off in the test.

 the total percentage of students clearing the cut off in the test is 65%

Calculation:

Let's assume there were b boys and g girls in the test.

According To question:

the total number of students who cleared the cut off = (60/100)b + (80/100)g = 0.65 * 400

the total number of students who took the test =  b + g = 400 

⇒ b = 400 - g

Substituting this value of b in the first equation:

(60/100)(400 - g) + (80/100)g = 0.65 * 400

Expanding and simplifying the equation:

240 - 0.6g + 0.8g = 260

0.2g = 20

g = 100

So, 100 girls appeared in the test.

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