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A sum of money is equally divided among a number of children. Had there been 10 children less, each…

Let there be n children sharing a sum S. From \(\frac{S}{n-10}=\frac{S}{n}+5\) we get \(S=\frac{n(n-10)}{2}\), and from \(\frac{S}{n+10}=\frac{S}{n}-3\) we get…

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A sum of money is equally divided among a number of children. Had there been 10 children less, each would have received ₹5 more, and had there been 10 children more each would have received ₹3 less. What is the sum of money that is distributed?

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Correct answer B

Let there be n children sharing a sum S. From Sn−10=Sn+5\frac{S}{n-10}=\frac{S}{n}+5 we get S=n(n−10)2S=\frac{n(n-10)}{2}, and from Sn+10=Sn−3\frac{S}{n+10}=\frac{S}{n}-3 we get S=3n(n+10)10S=\frac{3n(n+10)}{10}. Equating gives 10(n−10)=6(n+10)10(n-10)=6(n+10), so n=40n=40 and S=40×302=600S=\frac{40\times30}{2}=600.

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