Question

Ratio of ages of A 5 years hence to B’s age 3 years ago is 5 : 3. Also ratio of ages of A 4 years ago to B’s age 2 years hence is 4 : 5. Find the age of the elder.​

Answer 1

Step-by-step explanation:

Given : The ratio between the present ages of A and B is 5 : 3

Let the present age of A is 5x years

Let the present age of B is 3x years

Given : The ratio between A’s age 4 years ago and B’s age 4 years hence is 1:1

A’s age 4 years ago = 5x - 4

B’s age 4 years hence = 3x + 4

5x-4 = 1 ; 3x +4 = 1

5x-4/3x +4= 1/1

5x – 3x = 4 + 4⇒ 2x =8 x = 4

To find :

5x+4 = ? : 3x - 4 = ?

20 + 4 = 24 : 12 – 4

24 : 8

⇒3 : 1

Answer 2

'A' is the elder one having the age of 20 years.

Given: Ratio of ages of 'A' 5 years from now to that of 'B' 3 years ago is 5 : 3. Also, the ratio of ages of 'A' 4 years ago to that of 'B'  2 years from now is 4:5.

To Find: Age of the elder one.

Solution: Let A's present age be $x$ years and B's present age be $y$ years.

So, age of 'A' after 5 years $= x+5$ years

Also, age of 'A' 4 years ago $=x-4$ years

And, age of 'B' 3 years ago $=y-3$ years

Also, age of 'B' after 2 years $=y+2$ years

Now,

According to the question,

$\frac{x+5}{y-3} =\frac{5}{3}$

On cross multiplication,

$3(x+5)=5(y-3)$

$3x+15=5y-15$

$3x+30=5y$

$y=\frac{3x+30}{5}$ , let this equation of $y$ in terms of $x$ be equation (1)

Now, again using the given condition, we have

$\frac{x-4}{y+2} =\frac{4}{5}$

On cross multiplication,

$5(x-4)=4(y+2)$

$5x-20=4y+8$

$5x=4y+28$

Putting the value of $y$ in terms of $x$ from equation (1) into the above equation,

$5x=\frac{4(3x+30)}{5} +28$

Multiplying the whole equation by 5,

$25x=4(3x+30)+140$

$25x=12x+120+140$

$13x=260$

$x=20$

Putting the value of $x$ in equation (1), we get

$y=\frac{3(20)+30}{5}$

$y=\frac{60+30}{5}$

$y=\frac{90}{5}$

$y=18$

So, 'A' is 20 years old and 'B' is 18 years old.

Hence, A is the elder one, and A's age is 20 years.