Question

250 is divided equally among a certain
number of children. If there were 25 children
more, each would have received 50 paise less.
Find the number of children.
nonces the weekly
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Answer 1

Answer:

total number of children = 100

Step-by-step explanation:

let no of children = x

total amount = 250

share for each child = 250/x

no of children with 25 more children = x+25

share for each child now = 250/(x+25)

given, 250/(x+25) = 250/x - 1/2. [50 paise = 1/2 rupees]

=> 250/x - 250/(x+25) = 1/2

=> 250×2{1/x - 1/(x+25)} = 1

=> 500{(x+25)-x}/{x(x+25)} = 1

=> 500×25 = x(x+25)

=> 12500 = x^2 + 25x

=> x^2 + 25x - 12500 = 0

=> x = {-25 +- √(625 + 50000)}/2

=> x = {-25 +- √50625}/2

=> x = {-25 +- 225}/2

=> x = {-25 + 225}/2 or x = {-25 - 225}/2

=> x = 100 or x = -125 (no of negative children is impossible)

So total number of children = 100