Question

5 years ago Ahsan's age was 7 times of Shakeel's age but after 3 years
Ahsan's age will be 4 times of Shakeel's age. Calculate their ages.?​

Answer 1

Given:

5 years ago Ahsan's age was 7 times of Shakeel's age but after 3 years

Ahsan's age will be 4 times of Shakeel's age

To find:

Their ages

Solution:

Let's assume,

"x" years → the present age of Ahsan

"y" years → the present age of Shakeel

5 years ago:

Ahsan's age = (x - 5) years

Shakeel's age = (y - 5) years

So, according to the question, we can form an equation as:

(x - 5) = 7(y - 5)

⇒ x - 5 = 7y - 35

⇒ x - 7y = -30 ....... (i)

After 3 years:

Ahsan's age = (x + 3) years

Shakeel's age = (y + 3) years

So, according to the question, we can form an equation as:

(x + 3) = 4(y + 3)

⇒ x + 3 = 4y + 12

⇒ x - 4y = 9 ....... (ii)

Now, on subtracting eq. (i) & (ii), we get

x - 7y = -30

x - 4y = 9

-    +      -

--------------------

 - 3y = - 39

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∴ y = $\frac{39}{3}$ = 13

On substituting the value of y = 13 in ( ),we get

x - 7(13) = -30

⇒ x - 91 = - 30

⇒ x = - 30 + 91

⇒ x = 61

Thus, Ahsan's present age is 61 years and Shakeel's present age is 13 years.

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