Question

6 years ago, three times the age of B was 2 years more than the age of A's that time. 6 years from now, twice the age of B will be equal to A's age at that time. Find the sum of their ages.​

Answer 1

➱ Given :-

• 6 years ago, 3 times the age of B was 2 years more than the age of A

• 6 years from now, Twice the age of B will be equal to A's age

➱ To Find :-

• Sum of the ages of A and B

➱ Solution :-

➻ Let the ages of A and B be a & b years respectively

➻ Then, 6 years ago their ages will be a - 6 and b - 6

➻ And, 6 years from now their ages will be a + 6 and b + 6

Now, According to the question,

6 years ago,

$\implies\sf{3 ( b - 6 ) = 2 + ( a - 6 )}$

$\implies\sf{3b - 18 = a - 4}$

$\implies\sf{3b - 18 + 4 = a}$

$\implies\sf{3b - 14 = a ---- ( 1 ) }$

6 years from now,

$\implies\sf{2 ( b + 6 ) = a + 6}$

$\implies\sf{2b + 12 = a + 6 ---- ( 2 )}$

Now, By substituting value of a from equation ( 1 ) we get,

$\implies\sf{2b + 12 = 3b - 14 + 6 }$

$\implies\sf{2b + 12 = 3b - 8 }$

$\implies\sf{12 + 8 = 3b - 2b }$

$\implies\sf\pink{ 20 = b }$

Now, By substituting values of b to equation ( 1 ) to find 'a' we get,

$\implies\sf{3 × 20 - 14 = a}$

$\implies\sf{ 60 - 14 = a}$

$\implies\sf\pink{ 46 = a}$

Hence, The required ages are,

✰ Age of A = 46 years

✰ Age of B = 20 years

Sum of their ages = 46 + 20 = 66 years

Hence, The sum of the ages of A and B is 66 years

Answer 2

Answer:

Answer in attachment. ( 3 attachment)

Hope it will help you.