Question

20. A man is 3 timnes as old as his daughter. After 10 years he will be twice as old as his daughter. Find the daughter's present age.​

Answer 1

$\huge\purple{Required \: Answer :}$

Let,

The Age Of Man be $x$

The Age of Daughter be $y$

From Condition 1,

$x = 3y \: \: \: \: \: \: \: \\ x - 3y = 0$

From Condition 2,

$( \: x + 10 \: ) = 2 \: ( \: y + 10 \: ) \\ x + 10 = 2y + 20 \\ x - 2y = 20 - 10 \\ x - 2y = 10$

Subtract Equation 1 From Equation 2 :-

$\: \: \: \: \: \: \: \: \: \: x - 2y = 10 \\ \: \: \: - \: \: \: x - 3y = 0 \: \\ \: \: \: \: \: \: \: \: \: \: \: = \: \: \: \: y = 10$

Put y = 10 in equation 1 ,

$x - 3y = 0 \\ x - 3(10) = 0 \\ x - 30 = 0 \\ x = 30$

Hence,

The Present Age of Man is $\LARGE{30}$ Years And The Present Age of Daughter is $\LARGE{10}$ Years.

$\huge{Thanks}$