The sums of ages of two of them at a time are 4 years, 6 years and 8 years

There are three brothers. The sums of ages of two of them at a time are 4 years, 6 years and 8 years. The age difference between the eldest and the youngest is
(a) 3 years
(b) 4 years
(c) 5 years
(d)( 6 years

Anurag Mishra Professor Asked on 19th February 2016 in Maths.
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  • 1 Answer(s)
    Best answer

    Answer: (b) 4 years

    Solution:-
    Lat the three brothers be A, B and C

    The sum of two of them at a time are 4 years, 6 years and 8 years.
    Then,  A + B = 4  ……………………….. (1) 
    B + C = 6 ……………………………………… (2) 
    C + A = 8 …………………………………..(3) 

    From equation (1), 
    A = 4 – B

    Put the value of A = 4 – B in equation (3),  
    Then,  C + 4 – B = 8 
     C – B = 8 – 4
    C – B = 4 ………………………………(4) 

    Add, equation (2) & (4), 
    B + C + C – B = 6 + 4
     2 C = 10
    C = 10/2
    C = 5 years

    Put the value of C in equation (2), 
    Then, B +5 = 8 
    B = 8 – 5
    B = 3 years

    Put the value of A in equation (1), 
    Then, 3 + A = 4
    A = 4 – 3
     A = 1 years

    Thus, the ages of the three brothers are 1 years, 3 years and 5 years. 

    So, the age difference between the eldest and smallest = 5 – 1 
     = 4 years. 

    Hence, the correct answer is option (b) 4 years. 

    Anurag Mishra Professor Answered on 19th February 2016.
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