Question

In an examination 30,000 candidates appeared from Gujarat, Exam is in three languages Hindi, English, Gujarati and (before starting examination candidate choose individual language and in between examination changing language is allowed), 53% of candidates complete the exam in English, 61% of candidate in Hindi, 60% of candidate in Gujarati, 24% of candidates complete examination in English and Hindi both, 27% of candidates complete examination in English and Gujarati both, 35% of candidates complete examination Hindi and Gujarati both. Find how many candidates complete the examination in single language?
1. 11,600
2. 10,400
3. 11,400
4. 12,000
5. None of these

Answer 1

Correct Answer - Option 3 : 11,400

Given:

Total candidates appeared in examination = 30,000

English = 53%

Hindi = 61%

Gujarati = 60%

Both Hindi & English = 24%

Both Hindi & Gujarati = 35%

Both Gujarati & English = 27%

Concept:

Diagram

When “all” value not given in above diagram than try to find the value of place where written all, after that we able to solve question on that.

For finding “all” place = total – full circles values individual + both value

Calculation:

Find place value of “all” = (100 – 53 – 61 – 60 + 27 + 24 + 35)

⇒ 12%

Now find the value of “only single” place = complete circle value – overlapping of circle

Diagram

So, only English = (53 – 12 – 12 – 15)

⇒ 14%

Only Hindi = (61 – 12 – 12 – 23)

⇒ 14%

Only Gujarati = (60 – 12 – 15 – 23)

⇒ 10%

Total percentage of only single subject = only English + only Hindi + only Gujarati

⇒ 14 + 14 + 10

⇒ 38%

So, 38% of 30,000

⇒ 11,400 candidates

∴ 11,400 candidates complete examination in only single subject