Question

A father is 3 times as old as his son, 9 years ago the father was 4 times as old

as his son. find their present ages.​

Answer 1

`\bold{\huge{\green{\underline{ Solution }}}}`

Given :-

• We have given in the question that, A father is 3 times as old as his son
• 9 years a ago, The father was 4 times as old as his son

To Find :-

• We have to find the present ages of son and father

Let's Begin :-

Let the present age of son be x

• A father is 3 times old as his son

Therefore,

Present age of the father will be

`\bold{ = 3x\:\: years }`

9 years ago,

The age of the son was

`\bold{ = ( x - 9)\: years}`

So,

Age of the father was

`\bold{ = 3(x - 9) \:years ...eq(1)}`

But,

• It is given that, 9 years a ago father was 4 times as old his son age
• That is,
  `\bold{ 4(x - 9) ...eq(2)}`

From eq(1) and eq(2) :-

`\sf{3(x - 9) = 4(x - 9)}`

`\sf{3x - 27 = 4x - 36}`

`\sf{3x - 4x = -36 + 27}`

`\sf{-x = -9 }`

`\bold{\pink{ x = 9 \: years }}`

Thus, The present age of the son is 9 years

Therefore,

Age of the father will be

`\sf{ = 3 × 9 }`

`\bold{\red{ = 27 \: years }}`

Hence, The present ages of son and father is 9 years and 27 years