Question

Rs 6500 is divided equally among a certain number of persons. had there been 15 more persons. each would have got rs 30 less. find original number of persons.

Answer 1

Answer:

Explanation:

Solution :-

Let total number of persons be x.

Each person gets = Rs. 6500/x

Under new conditions,

Each person gets Rs 6500/x + 15

According to the Questions,

⇒ 6500/x - 6500/x+15 = 30

⇒ 6500(x + 15) - 6500x/x(x + 5) = 30

⇒ 6500x + 15 × 6500 - 6500x = 30(x² + 15x)

⇒ 15 × 6500 = 30(x² + 15x)

⇒ x² + 15x = 3250

⇒ x² + 15x - 3250 = 0

⇒ x² + 65x - 50x - 3250 = 0

⇒ x(x + 65) - 50(x + 65) = 0

⇒ (x - 50) (x + 65) = 0

⇒ x = 50, - 65 (Neglecting negative sign)

⇒ x = 50

Hence, the original number of persons is 50.

Answer 2

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QUESTION :

Rs 6500 is divided equally among a certain number of persons. had there been 15 more persons. each would have got rs 30 less. find original number of persons.

SOLUTION :

Suppose that the original number of persons is X

=> Each Person Gets : Rs. [ { 6500 } / X ] .......[ 1 ]

Now suppose that there are 15 more person's.

Now Total Number Of Person's = X + 15

=> Now Each person Gets : Rs. [ { 6500 } / { X + 15 } ] ......[ 2 ]

Difference between [ 1 ] and [ 2 ] = 30

=> [ { 6500 } / { X + 15 } ] - [ { 6500 } / X ] = 30

=> [ 6500 × 15 ] / [ n ^2 + 15 n ] = 30

=> n^2 + 15 n - 3250 = 0

=> n^2 + 65 n - 50 n - 3250 = 0

=> n ( n + 65 ) - 50 ( n + 65 ) = 0

=> ( n - 50 ) ( n + 65 ) = 0

=> n = 50 as n can't be negative...

So the original number is person's = 50.....( A)