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Question
The ratio of passed and failed students in an examination was 3 : 1. Had 30 less appeared and 10 less failed, the ratio of passes to failures would have been 13 : 4. Find the number of students who appeared for the examination.
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Solution
Let the number of passed students be x and the number of failed students be y.
According to the question,
`x/y = (3)/(1)`
⇒ x = 3y ....(i)
Now, if 30 less appeared and 10 less failed, then we have
Number of students appeared = x + y - 30
number of failed students = y - 10
∴ number of passed students = x - 20
⇒ `(x - 20)/(y - 10) = (13)/(4)`
⇒ 4x - 80 = 13y - 130
⇒ 4x - 13y = -50
⇒ 4(3y) - 13y = -50 ...[From (i)]
⇒ 12y - 13y = -50
⇒ -y = -50
⇒ y = 50
⇒ x = 3 x 50 = 150
⇒ x + y
= 150 + 50
= 200
Hence, 200 students appeared for the examination.
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