Question

The sum of ages of A, B and C is equal to age of D. Ten years later the ratio of sum of ages of A, B
and c to the age of D is 5:3. Present age of D is equal to.​

Answer 1

Given :

The sum of ages of A, B and C is equal to age of D. Ten years later the ratio of sum of ages of A, B and C to the age of D is 5 : 3.

To Find :

Present age of D.

Solution :

Let the present ages of A, B, C and D be x, y, z and w respectively.

Given that, sum of present ages of A, B, and C is equal to age of D.

So we can say that,

➝ x + y + z = w .......... (I)

Ten years laters,

• Age of A will be (x + 10) years

• Age of B will be (y + 10) years

• Age of C will be (z + 10) years

• Age of D will be (w + 10) years

After ten years the ratio of sum of ages A, B, C to the age of D is 5 : 3

$\sf:\implies\:\dfrac{(x+10)+(y+10)+(z+10)}{w+10}=\dfrac{5}{3}$

$\sf:\implies\:\dfrac{(x+y+z)+30}{w+10}=\dfrac{5}{3}$

From the first equation, x + y + z = w

$\sf:\implies\:\dfrac{w+30}{w+10}=\dfrac{5}{3}$

$\sf:\implies\:3(w+30)=5(w+10)$

$\sf:\implies\:3w+90=5w+50$

$\sf:\implies\:2w=40$

$:\implies\:\underline{\boxed{\bf{\purple{w=20\:yrs}}}}$

∴ Present age of D is 20 yrs.