Question

ram's father is 4times as old as ram . 5 year ago , his father was 9 times as old as he was then find there present age​

Answer 1

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✤ Required Answer:

✒️ GiveN:

• Ram's father is 4 times as old as Ram.
• 5 years ago, he was 9 times as old as Ram.

✒️ To FinD:

• Find the present ages of Ram and his father...?

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✤ How to solve?

For solving this, we need to consider the ages of Ram and his father be two variables. Then, according to conditions given, we will be able to form 2 simultaneous linear equations. Then we can solve it by Elimination or Substitution method.

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✤ Solution:

Let,

• Age of Ram be x
• And, Age of his father be y

Then,

According to condition-1

➝ Age of father = 4 × Age of Ram

➝ y = 4x

➝ y - 4x = 0 -------(1)

According to condition-2

➝ Age of father 5 years ago = 9 × Age of ram 5 years ago.

• Age of Ram 5 years ago = x - 5
• Age of Father 5 years ago = y - 5

Then,

➝ y - 5 = 9(x - 5)

➝ y - 5 = 9x - 45

➝ y - 9x = -45 + 5

➝ y - 9x = -40 -------(2)

Subtracting eq.(2) from eq.(1),

➝ y - 4x - (y - 9x) = 0 -(-40)

➝ y - 4x - y + 9x = 40

➝ 5x = 40

➝ x = 8

Putting in eq.(1),

➝ y - 4(8) = 0

➝ y - 32 = 0

➝ y = 32

So, The correct answer is:

• Age of Ram = $\red{\rm{8}}$

• Age of Ram's father =  $\red{\rm{32}}$

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Answer 2

$\huge \tt \underline{ \underline \green{ Given }}$

1. Ram's father is 4 times older than Ram.
2. 5 years ago, he was 9 times older than Ram.

$\huge \tt \underline{ \underline \blue{ Find}}$

1. Their present ages.

$\huge \tt \underline{ \underline \red{ Solution}}$

Let, the age of Ram = a years

age of Ram's father = b years

ACCORDING TO QUESTION

4a = b --------(i)

b - 5 = 9(a - 5)

b - 5 = 9a - 45

collect like terms

b - 9a = - 45 - 5

b - 9a = - 40 ---------(ii)

Now, in eq (i)

$4a = b \\ a = \frac{b}{4}$

put the value of a in eq (ii)

$b - 9a = - 40 \\ \implies b - 9( \frac{b}{4} ) = - 40 \\ \implies b - \frac{9b}{4} = - 40 \\ \implies \frac{4b - 9b}{4} = - 40 \\ \implies \frac{ - 5b}{4} = - 40 \\ \implies b = \cancel{- 40} \times \frac{4}{ \cancel{- 5} } \\ \implies b = 32 \: years$

substitute value of b in eq (i)

$\rightarrow 4a = b \\ \rightarrow 4a = 32 \\ \rightarrow a = \frac{ \cancel{32}}{ \cancel{4} } \\ \rightarrow a = 8 \: years$

$So, \: present \: age \: of \: Ram's \: father = \\ \boxed{\tt32years} \\ \\ present \: age \: of \: Ram = \\ \boxed{\tt8years}$