Question

12 years ago, age of Ahmad was 3 times the age of Qadeer. After 12 years, ratio of ages of Qadeer to Ahmad will be 2:3. What is the present age of Ahmad?​

Answer 1

Answer:

48 and 72

Step-by-step explanation:

Let Qadeer' s age be x,

Then, Ahmad's age will be 3x

Ahmad's age after 12 years = 3x + 12

Qadeer's age after 12 years = x + 12

Ratio of present ages of Qadeer and Ahmad = 2x : 3x

Sum of ratio of present ages of Qadeer and Ahmad = 2x + 3x

= 5x

A.T.Q

3x + 12 + x + 12 = 5x

4x + 24 = 5x

5x - 4x = 24

x = 24

Present age of Qadeer = 2x

= 2 × 24

= 48

Present age of Ahmad = 3x

= 3 × 24

= 72

Answer 2

Given :

Ratio of ages , 12 years later : 2:3

Age of Ahmed is 3 times Qadeer, 12 years ago.

To find :

The present age of Ahmed.

Solution :

Let the age of Qadeer be x years.

Let the age of Ahmed be 3x years.

Total gap of years :

$\sf \dashrightarrow 12 + 12$

$\sf \dashrightarrow 24 years$

According to the question,

$\sf \dashrightarrow x + 24 : 3x + 24 = 2:3$

$\sf \dashrightarrow \dfrac{x + 24}{3x + 24} = \dfrac{2}{3}$

$\sf \dashrightarrow 3(x + 24) = 2(3x + 24)$

$\sf \dashrightarrow 3x + 72 = 6x + 48$

$\sf \dashrightarrow 3x - 6x = 48 - 72$

$\sf \dashrightarrow -3x = -24$

$\sf \dashrightarrow x = \dfrac{-24}{-3}$

$\sf \dashrightarrow x = 8$

Now, let's find the age of Ahmed and Qadeer.

Age of Qadeer (12 years ago) :

$\sf \dashrightarrow x = 8$

Age of Ahmed (12 years ago) :

$\sf \dashrightarrow 3x = 3(8)$

$\sf \dashrightarrow 24$

Now, we can find the present ages of both.

Present age of Qadeer :

$\sf \dashrightarrow 8 + 12$

$\sf \dashrightarrow 20 \: years$

Present age of Ahmed :

$\sf \dashrightarrow 24 + 12$

$\sf \dashrightarrow 36 \: years$

Hence, present age of Ahmed the is 36 years.