# the average age of three friends

Three friends Rajan, Rakesh and Mukesh are childhood friends. They remember that, three years ago the average of their ages was 27 years. While Rakesh and Mukesh remember that five years ago the average age of them was 20 years only. How old is Rajan now?

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solution

a, b, and c represent current ages of three friends

three years ago, the equation of average would look like this;

((a+b+c)-9)/3=27;

(a+b+c)=72………..(1)simplified

average of two friends five yrs ago:

((a+b)-10)/2=20

(a+b)=50……………(2)simplified

therefore

(50+c)=72…………(3) derived

hence from equ. 3, c=22

the age of the third person is 22 years.

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(a+b+c)=72…..wrong

(a+b+c)=90

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nope…

You can check this solution:

3 years ago the sum of their (Rajan, Rakesh and Mukesh) ages was: 27 x 3 = 81 years

• The sum of their present ages is: 81 + 3 + 3+ 3 = 90 years…………….(1)

• 5 years ago the sum of ages of Rakesh and Mukesh was: 20 x 2 = 40 years

• So sum of present ages of Rakesh and Mukesh is: 40 +5 +5 = 50 years…………(2)

• The difference of 1 and 2 equation gives the present age of Rajan.: 90 – 50 = 40 years

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most correct, thanks

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solution-modified

a, b, and c represent current ages of three friends

three years ago, the equation of average would look like this;

((a+b+c)-9)/3=27;

(a+b+c)=90………..(1)simplified

average of two friends five yrs ago:

((a+b)-10)/2=20

(a+b)=50……………(2)simplified

therefore

(50+c)=90…………(3) derived

hence from equ. 3, c=40

the age of the third person(Rajan) is 40 years.

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