In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates ...
In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how many candidates applied for the examination?
Answer/Solution
30000
Steps/Work
Explanation :
Let the number of candidates applied for the examination = x
Given that 5% of the applicants were found ineligible.
It means that 95% of the applicants were eligible (∴ 100% - 5% = 95%)
Hence total eligible candidates = 95x/100
Given that 85% of the eligible candidates belonged to the general category
It means 15% of the eligible candidates belonged to other categories(∴ 100% - 85% = 15%)
Hence Total eligible candidates belonged to other categories
= total eligible candidates × (15/100) = (95x/100) × (15/100)
= (95x × 15)/(100 × 100)
Given that Total eligible candidates belonged to other categories = 4275
⇒ (95x × 15)/(100 × 100) = 4275
⇒ (19x × 15)/(100 × 100) = 855
⇒ (19x × 3)/(100 × 100) = 171
⇒ (x × 3)/(100 × 100) = 9
⇒ x/(100 × 100) = 3
⇒ x = 3 × 100 × 100 = 30000
Answer : Option B
Let the number of candidates applied for the examination = x
Given that 5% of the applicants were found ineligible.
It means that 95% of the applicants were eligible (∴ 100% - 5% = 95%)
Hence total eligible candidates = 95x/100
Given that 85% of the eligible candidates belonged to the general category
It means 15% of the eligible candidates belonged to other categories(∴ 100% - 85% = 15%)
Hence Total eligible candidates belonged to other categories
= total eligible candidates × (15/100) = (95x/100) × (15/100)
= (95x × 15)/(100 × 100)
Given that Total eligible candidates belonged to other categories = 4275
⇒ (95x × 15)/(100 × 100) = 4275
⇒ (19x × 15)/(100 × 100) = 855
⇒ (19x × 3)/(100 × 100) = 171
⇒ (x × 3)/(100 × 100) = 9
⇒ x/(100 × 100) = 3
⇒ x = 3 × 100 × 100 = 30000
Answer : Option B