Rs. 9,000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less. Find the original number of persons.
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there were 50 people . bec 50-20=30 .
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Let the original number of students = x
Total amount to be divided = Rs. 9000
share of each student = Rs. [9000x]
When the number of students increased by 20 :
number of students = (x + 20)
share of each student =Rs. [9000x + 20]According to the question,9000x − 9000x+20 = 160⇒9000[1x − 1x + 20] = 160⇒[1x − 1x + 20] = 1609000⇒[x + 20 − xx (x + 20)] = 4225⇒20x2+ 20x = 4225
⇒x2 + 45x − 25x − 1125 = 0⇒x(x + 45) − 25(x + 45) = 0⇒(x − 25) (x + 45) = 0⇒x − 25 = 0 or x + 45 = 0⇒x = 25 or x = −45 [rejected]So, original number of students = 25
Total amount to be divided = Rs. 9000
share of each student = Rs. [9000x]
When the number of students increased by 20 :
number of students = (x + 20)
share of each student =Rs. [9000x + 20]According to the question,9000x − 9000x+20 = 160⇒9000[1x − 1x + 20] = 160⇒[1x − 1x + 20] = 1609000⇒[x + 20 − xx (x + 20)] = 4225⇒20x2+ 20x = 4225
⇒x2 + 45x − 25x − 1125 = 0⇒x(x + 45) − 25(x + 45) = 0⇒(x − 25) (x + 45) = 0⇒x − 25 = 0 or x + 45 = 0⇒x = 25 or x = −45 [rejected]So, original number of students = 25
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