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The sum of the ages of 22 boys and 24 girls is 160.What is the sum of ages of one boy plus one girl, if all the boys are of the same age and all the girls are of the same age, and only full years are counted?
Re: PS - Age problem [#permalink]
27 Mar 2009, 12:53
OA : - C.
Here is my approach: -
22B + 24G = 150. (B and G are integers) ==> 11B + 12G = 80. ==> 11(B+G) +G = 80 ==> B+G = (80-G) / 11. Since B and G are intergers, then B + G must be an integer ==> 80 - G must be a multiple of 11. This implies G is the reaminder left when 80 is divided by 11. Ie G = 3.
Substituting G in B +G we get (80 - 3) / 11 = 7 which is the ans.
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