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A Foreign Missionary school has 2001 scholars. The percentage of scholars of this school who study Farsi is between 80 and 85 and the percentage of the scholars of the school who study Swiss is between 30 and 40. Each scholar of this school studies at least one of the two languages. What is the absolute difference between the minimum and maximum possible numbers of scholars who study both Farsi and Swiss?

A Foreign Missionary school has 2001 scholars. The percentage of scholars of this school who study Farsi is between 80 and 85 and the percentage of the scholars of the school who study Swiss is between 30 and 40. Each scholar of this school studies at least one of the two languages. What is the absolute difference between the minimum and maximum possible numbers of scholars who study both Farsi and Swiss? Correct Answer 298

Calculation:

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⇒ f = Farsi alone, s = Swiss alone and x = both Farsi and Swiss
⇒ F lies between 80% to 85% of 2001
or 1601 ≤ F ≤ 1700  
⇒ Similarly for Swiss (S)
⇒ 601 ≤ S ≤ 800 

⇒ F = f + x and S = s + x

⇒ We also have: f + s + x = 2001
⇒ 1201 ≤ f ≤ 1400
Similarly s = 2001 – (f + x)
⇒ 301 ≤ s ≤ 400
⇒ as x = 2001 – (f + s)

⇒ we have: x = {max = 2001 - min (f + s)} = 499

                        {min = 2001 - max (f + s)}  = 201   

⇒ 201 ≤ x ≤ 499
⇒ x can take a minimum value = 201 and x can take a maximum value = 499
⇒ the difference = 499 – 201 = 298.

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