Question

₹9000 were divided equally among a certain number of persons. Had there been 20 more persons each would have got ₹ 160 less. Find the original number of persons.​

Answer 1

Answer:

Original number of persons= 25

Step-by-step explanation:

Let the original no. of persons be x,

then 9000 divided equally between x persons, each one get ------> $\frac{9000}{x}$

9000 divided equally between (x + 20) persons, each one get------> $\frac{9000}{(x+20)}$

According to the que,

$\frac{9000}{(x+20)}$ = $\frac{9000}{x} -160$

=> 9000x = (x+20)(9000 - 160x)

=> 9000x = 9000x - 160x² + 180000 - 3200x

=> 160x²+ 3200x - 180000 = 0

=> x² + 20x - 1125 = 0

=> x² + 45x - 25x - 1125 = 0

=> x(x + 45) - 25(x + 45) = 0

=> (x + 45)(x - 25) = 0

   Either (x + 45) = 0 or ( x - 25) = 0

   (x + 45) = 0 => x = - 45 (It is not possible because it is negative)

   ∴ (x - 25) = 0 => x = 25. ans

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Answer 2

Answer:

9000 were divided equally among a certain number of persons. Had there been 20 more persons each would have got ₹ 160 less. Find the original number of persons.