Question

Now the age of ayushi is half of his father's age.Twenty years ago She was 1/4 of his father's age .What will be the age of ayushi after 10 years?

Answer 1

$\textbf {Hey there, here is the solution.}$

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STEP 1: Define x:

Let Ayushi's age be x

His father = 2x

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STEP 2: Find their age 20 years ago in term of age:

Ayushi = x - 20

Father = 2x - 20

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STEP 3: Form equation:

20 years ago, Ayushi is 1/4 of his father's age:

x - 20 = 1/4(2x -20)

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STEP 4: Solve x:

x - 20 = 1/4(2x -20)

Multiply by 4 on both sides:

4x - 80 = 2x - 20

Subtract 2x:

2x - 80 = -20

Add 80 to both sides:

2x = 60

Divide both sides by 2:

x = 30

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STEP 5: Find Ayushi's age 10 years later:

Ayshui = x + 10 = 30 + 10 = 40 years old

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$\textbf {Cheers}$

Answer 2

HELLO FRIEND HERE IS YOUR ANSWER,,,,,

Let father's age be variable "x" and Ayushi's age be x/2, that is,,

Father's age = x

Ayushi's age = x/2

After 20 years,,,

$fathers \: \: age = x - 20 \\ \\ ayushis \: \: age = \frac{x}{2} - 20$

We know that Ayushi's age was 1/4 of her Father's age, therefore,,,,,

$= > \frac{1}{4} ( x - 20) = \frac{x}{2} ( - 20)$

Subtract x/2 from both left and right hand sides,,,

$= > \frac{1}{4} (x - 20) - \frac{x}{2} = \frac{x}{2} - 20 - \frac{x}{2}$

By simplifying it,,,,,

$\frac{1 \times (x - 20)}{4} - \frac{x}{2} = \frac{x}{2} - \frac{x}{2} - 20$

Use LCM of that and prime factorisation, that is, 2 × 2.

$= > \frac{(x - 10)}{4} - \frac{x \times 2}{2 \times 2} = 0 - 20$

$= > \frac{x - 20}{4} - \frac{x \times 2}{4} = 0 - 20 \\ \\ \\ = > \frac{x - 20 - xx2}{4} = - 20 \\ \\ \\ = > \frac{x - 2x - 20}{4} = - 20 \\ \\ \\ = > \frac{ - x - 20}{4} = - 20$

Multiply both right and left hand sides by the value or a number of "4".

$= > \frac{4( - x - 20)}{4} = 4( - 20)$

Simplifying it, we get,,,

$= > - x - 20 = - 80$

Add the value or number of "20" to both the sides,,,

$= > \: - x - 20 + 20 = - 80 + 20$

Simplify,,,

$= > \: \: - x = - 60$

Divide both the sides by the value or number of "-1".

$= > \: \: \frac{ - x}{ - 1} = \frac{ - 60}{ - 1 }$

Hence, by simplifying it, we get,,,,

$= > \: \: \: x = 60$

Therefore, the Father's age is = 60

Therefore, Ayushi's age will become,,,

$= > \: \: \frac{x}{2} \\ \\ x = 60 \\ \\ \\ therefore. \\ \\ \\ = > \: \: \frac{60}{2} = 30$

And,, after $\textbf{10 years}$ , Ayushi's age will be,,,

$= > \: \: \: 30 + 10 = 40$

Which is the required solution for this type of question.

HOPE IT HELPS AND CLEARS YOUR DOUBTS FOR USING VARIABLES TO SOLVE IN A UNIQUE METHOD!!!!!