### 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.