Question

10 years ago, the ratio of age of A and B was 3:2 and after 10 years, their ages ratio will become 4:3. Find the sum of their present ages​

Answer 1

Step-by-step explanation:

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Answer 2

The sum of their present ages​ is 120 .

Explanation:

Let the present ages of A and B are x and y.

According to the given statement , we have

$\dfrac{x-10}{y-10}=\dfrac{3}{2}$

$2(x-10)=3(y-10)$

$2x-20=3y-30$            

$2x-3y=-10$                 (1)

$\dfrac{x+10}{y+10}=\dfrac{4}{3}$      

$3(x+10)=4(y+10)$

$3x+30=4y+40$

$3x-4y=10$                  (2)

Multiply 3 to equation (1) and 2 to the equation (2), we get

$6x-9y=-30$        (3)

$6x-8y=20$     (4)

Subtract (3) from (4) , we get

$y=20-(-30)=20+30=50$

Put y= 50 in (1) , we get

$2x-3(50)=-10$  

$2x-150=-10$  

$2x=-10+150=140$  

$x=70$  (Divide both sides by 2)

The sum of present ages = x+y= 50+70 = 120.

Hence, the sum of their present ages​ is 120 .

# Learn more :

Present age of rohit is two times the present age of mohit if the sum of their present age is 36 years then find their present ages​

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