Question

please give answer it's urgent​

Answer 1

Given :-

• The present age of Natia and his father are in the ratio 1 : 3
• After 10 years the ratio of their ages becomes 1 : 2

To Find :-

• Their present age

Required Answer ;-

• We can asume that the present age of Natia is x
• According to the question,

• In First case
• The present age of Natia and his father are in the ratio 1 : 3
• hence we can write it like this,
• ratio of their age = x / 3x
• here x = age of Natia
• . 3x = age of Natia's father

• In Second case
• After 10 years the ratio of their ages becomes 1 : 2
• Natia's age = x + 10
• Natia's father's age = 3x + 10
• The total ratio of age 1 : 2 ( given in question )
• hence ,
• (x + 10) / (3x + 10 ) = 1 / 2

Now we solve this equation then,

$\large\tt \green{ \frac{x + 10}{3x + 10} = \frac{1}{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large\tt \green{2( x + 10) =1 (3x + 10)} \: \\ \\ \large\tt \green{2x + 20 = 3x + 10} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large\tt \green{20 - 10 = 3x - 2x} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large\tt \green{10 = x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \\ \large\tt \red{hence} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large\tt \blue {\fbox{age \: \: of \: \: natia = 10 \: years}}$

$\large\tt \green{age \: \: of \: \: natia's \: \: father's = 3x} \\ \\ \large\tt \green{ = 3x} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large\tt \green{ = 3(10)}\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large\tt \green{ = 30} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large\tt \red{ hence} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large\tt \blue{ \fbox{age \: \: of \: \: natia's \: \: father's =30 \: years }}$

I hope it helps you ❤️✔️