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# Ancestry

A man who is aged between 50 & 70, and has a very large number of grandsons , said 'Each of my sons has as many sons as brothers, and the combined number of my sons and grandsons is exactly my age'. How old is the man and how many grandsons does have?

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Note by Sharath Chandar
3 years, 11 months ago

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let x be the age of the man

n be the number of sons

no. of brothers for each son = n-1 = no. of sons for each son

=> total no. of grandsons = n*(n-1)

sons + grandsons = age

=> n + n*(n-1) = x

x = n^2

since n is an integer, the only perfect square between 50 and 70 is 64.

=> age = 64

grandsons = 56

- 3 years, 11 months ago

Thank you very much!!!!!

- 3 years, 11 months ago

64 and 57

- 3 years, 11 months ago

the man is 64 years old and has 56 grandsons

- 3 years, 11 months ago

can u post how how u solved this problem..

- 3 years, 11 months ago