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Mughilan S. , asked a question
Subject: Math , asked on 15/1/13

Rs 6500 were divided equally among a certain no: of persons. Had there been 15 more persons each would have got rs 30 less. Find the original no: of persons

thank you ...waiting for your answer..

EXPERT ANSWER

Gursheen kaur , Meritnation Expert added an answer, on 21/1/13
1882 helpful votes in Math

Let the original number of persons be  n.

 

∴ Amount received by each person = 

 

If there were 15 more person, 

then

Number of persons =  n  + 15

 

New amount received by each person 

 

∴According to the question,

Amount received by each person – New amount received by each person = Rs 30

 

Thus, the original number of persons is 50.

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Tadepalli Manoj Ram From Delhi Public School ,farakka, added an answer, on 15/1/13
13 helpful votes in Math

let number of people be X. 

1st equation = 6500/X

2nd equation= 6500/ 15+X

asper question when 15 people werwe more then 30 rupees were less with everyone. 

therefore, 6500/X- 6500/ X+15 = 30

  6500(1/X-1/X+15) = 30

  6500(X+15- X / X2 + 15X) = 30

  6500(15/X2+ 15X)= 30

  6500(15) = 30(X2 + 15X)

  6500(15) = 30X2 +30(15X)  [TAKING 15 COMMON]

  6500  = 2X2  + 30X

  0  =  2X2 +30X - 6500 [TAKING 2 COMMON]

  0  =  X2 +15X - 3250

  0  = X2 +(65X - 50X) - 3250[MIDDLE TERM FACTORISATION]

  0  =  X2 +65X - 50X - 3250

  0  =  X(X +65) - 50(X+ 65)

  THEREFORE , X = 50 PEOPLE.

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