Question

the ages of ajay and Vijay are the ratio of 3:5 after 6 years from now their ages will be in the ratio of 3:4 .find their present ages?​

Answer 1

Given : The present ages of Ajay and Vijay are in the ratio 3: 5. After 6 years, their ages will be in the ratio 3 : 4.

To Find : Their present ages.

⠀⠀⠀____________________

Let's say their present ages be 3y and 5y

6 years from now,

$\:$

• Ajay's age = (3y + 6)
• Vijay's age = (5y + 6)

$\:$

❍ Also, given that their ages 6 years from now, will be in the ratio 3 : 4.

$\:$

$\sf \: : \implies \: \dfrac{(3y + 6)}{(5y + 6)} = \dfrac{3}{4}$

$\:$

$\sf : \implies \: 4(3y + 6) = 3(5y + 6)$

$\:$

$\sf : \implies \: 12y + 24 = 15y + 18$

$\:$

$\sf : \implies \: 24 - 18 = 15y - 12y$

$\:$

$\sf : \implies \: 3y = 6$

$\:$

$\sf : \implies \: y = \cancel\dfrac{6}{3}$

$\:$

$\sf : \implies \: y = 2$

⠀⠀⠀____________________

❍ Now, let's put the value of y in the present ages of Ajay and Vijay.

$\:$

• Present age of Ajay = 3y = 3(2) = 6 years
• Present age of Vijay = 5y = 5(2) = 10 years

$\: \:$

$\sf\therefore{\underline{Hence, \: the \: present \: ages \: of \: Ajay \: and \: Vijay \: are \: \bold{6 \: years} \:and \: \bold{10 \: years} \: respectively.}}$

Answer 2

Answer:

15 years

20 years

Step-by-step explanation:

Let the age of Ajay and Vijay be 3x and 4x

After 5 years their age are 3x+5 and 4x+5

ATQ

3x+5=4

4x+5=5

5(3x+5) = 4(4x+5)

15x+25 = 16x+20

x=5

So Ajay age is 3X5 = 15 years

So vijay age is 4X5= 20 years