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Rs. 250 is divided equally among a certain number of children. If there were 25 more children, each would have received 50 paise less. Find the number of children. |
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Answer» Let the number of children be x. It is given that Rs. 250 is divided equally amongst x childrens. ∴ Money received by each child = Rs. \(\frac{250}{x}\). If there were 25 more children then money received by each child = Rs. \(\frac{250}{x+25}\) From the given information, \(\frac{250}{x}\) - \(\frac{250}{x+25}\) = \(\frac{50}{100}\) ⇒ \(\frac{250(x+25)−250x}{ x(x+25)}\) = \(\frac{1}{2}\) ⇒ 2 × 6250 = x2 + 25x ⇒ x2 + 25x − 12500 = 0 ⇒ x2 + 125x − 100x − 12500 = 0 ⇒ x(x + 125) − 100(x + 125) = 0 ⇒ (x − 100)(x + 125) = 0 ⇒ x = 100 or x = −125. ∵ x ≠ −125 (Because number of children never be negative.) ∴ x = 100. Hence, The number of children is 100. |
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