Question

Ten years later, A will be twice as old as B and five years ago, A was three times as old as B. What are the present ages of A and B ?

A’s age = 50 years,and B’s age = 20 years

A’s age = 50 years,and B’s age = 25 years

A’s age = 30 years,and B’s age = 20 years

A’s age = 50 years,and B’s age = 30​

Answer 1

Step-by-step explanation:

Answer

A’s age = 50 years,and B’s age = 20 years

Answer 2

Solution :

Let the present age of A's be r years & the present age of B's be m years respectively.

$\underline{\underline{\tt{According\:to\:the\:question\::}}}$

$\underbrace{\bf{After\:10\:years\::}}$

The age of A will be (r+10) years .

The age of B will be (m+10) years .

Now;

$\mapsto\tt{(r+10) = 2(m+10)}\\\\\mapsto\tt{r+10 = 2m + 20}\\\\\mapsto\tt{r-2m = 20-10}\\\\\mapsto\tt{r-2m = 10}\\\\\mapsto\tt{r=10+2m ....................(1)}$

&

$\underbrace{\bf{5\:years\:ago\::}}$

The age of A was be (r-5) years .

The age of B was be (m-5) years .

Now;

$\mapsto\tt{(r-5) = 3(m-5)}\\\\\mapsto\tt{r-5 = 3m -15}\\\\\mapsto\tt{r-3m = -15 + 5}\\\\\mapsto\tt{r-3m = -10}\\\\\mapsto\tt{10+2m-3m =-10\:\:[from(1)]}\\\\\mapsto\tt{10-m=-10}\\\\\mapsto\tt{-m=-10-10}\\\\\mapsto\tt{\cancel{-}m=\cancel{-}20}\\\\\mapsto\bf{m=20\:years}$

∴ Putting the value of m in equation (1),we get;

$\mapsto\tt{r=10+2(20)}\\\\\mapsto\tt{r=10+40}\\\\\mapsto\bf{r=50\:years}$

Thus;

The present age of A's will be r = 50 years .

The present age of B's will be m = 20 years .