PROBLEM ON AGES




  1. Explanation :

    Let Rajeev's present age be x years. Then, Rajeev's age after 15 years = (x + 15) years. Rajeev's age 5 years back = (x - 5) years.

    	
     x + 15 = 5 (x - 5)
     x + 15 = 5x - 25 
    	 4x = 40 
    	  x = 10.
    Hence, Rajeev's present age = 10 years.






  1. Explanation :

    Let the age of the younger person be x years. Then, age of the elder person = (x + 16) years.

     
    3(x - 6) = (x + 16 - 6) 
       3x-18 = x + 10 
          2x = 28
           x = 14.
    Hence, their present ages are 14 years and 30 years.






  1. Explanation :

    Let Ankit's age be x years. Then, Nikita's age = 240/x years.

     
          2*(240 /x ) – x = 4 
              480 – x * x = 4x 
         x * x + 4x – 480 = 0
            ( x+24)(x-20) = 0 
                        x = 20.
    Hence, Nikita's age = 240 / 20 years = 12 years.






  1. Explanation :

    Sol. Let the son's present age be x years. Then, father's present age = (3x + 3) years
    (3x + 3 + 3) = 2 (x + 3) + 10
    3x + 6 = 2x + 16
    x = 10. Hence, father's present age = (3x + 3) = ((3 * 10) + 3) years = 33 years.






  1. Explanation :

    Let son's age 8 years ago be x years. Then, Rohit's age 8 years ago = 4x years. Son's age after 8 years = (x + 8) + 8 = (x + 16) years. Rohit's age after 8 years = (4x + 8) + 8 = (4x+ 16) years.

     2 (x + 16) = 4x + 16 
             2x = 16 
    	  x = 8 
    Hence, son's 'present age = (x + 8) = 16 years. Rohit's present age = (4x + 8) = 40 years.






  1. Explanation :

    . Let Gaurav's and Sachin's ages one year ago be 6x and 7x years respectively. Then, Gaurav's age 4 years hence = (6x + 1) + 4 = (6x + 5) years. Sachin's age 4 years hence = (7x + 1) + 4 = (7x + 5) years.
    \(\frac{6x+5}{7x+5}=\frac{7}{8}\) --> 8 (6x+5) = 7 (7x + 5) --> 48x + 40 = 49x + 35 --> x = 5.Hence, Sachin's present age = (7x + 1) = 36 years.






  1. Explanation :

    . Let the ages of Abhay and his father 10 years ago be x and 5x years respectively. Then, Abhay's age after 6 years = (x + 10) + 6 = (x + 16) years. Father's age after 6 years = (5x + 10) + 6 = (5x + 16) years.

     
        ( x + 16) =  3/7 *(5x + 16) 
       7 (x + 16) = 3 (5x + 16) 
         7x + 112 = 15x + 48
               8x = 64 
                x = 8.
    Hence, Abhay's father's present age = (5x + 10) = 50 years.