Question

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

Answer 1

Step-by-step explanation:

Call A and B the 2 present ages.

Ten years from now, A is twice as old as B

(A + 10) = 2(B + 10)................ (1)

Five years ago, A was 3 times as old as B

(A - 5) = 3(B - 5) .....................(2).

Solve the system (1) and (2).

From (2) --> A = 3B - 15 + 5 = 3B - 10.

Replace this value of A into (1) -->

3B - 10 + 10 = 2B + 20

B = 20

Present age of B is20.

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Answer 2

Answer

The present ages of A and B are 50 and 20 years respectively.

Given

• Ten years later , A will be twice as old as B
• Five years ago , A was three times as old as B

To Find

• The present ages of A and B

Solution

Let us consider the present ages of A and B are x and y years respectively

According to question

$\sf x + 10 = 2( y + 10) \\\\ \sf\implies x + 10 = 2y + 20 \\\\ \sf\implies x = 2y + 20-10 \\\\ \sf\implies x = 2y + 10 \dashrightarrow (1)$

Again by question

$\sf\implies x - 5 = 3(y - 5) \\\\ \sf{\underline{\dag \: \: Putting \: the \: value \: of \: x \: from \: (1) \: we \: have , }} \\\\ \sf\implies 2y + 10 - 5 = 3y - 15 \\\\ \sf\implies 2y + 5 = 3y - 15 \\\\ \sf\implies 2y - 3y = -15-5 \\\\ \sf\implies -y = -20 \\\\ \sf\implies y = 20$

★ Putting the value of y in (1)

$\sf\implies x = 2\times 20 + 10 \\\\ \sf\implies x = 40 + 10 \\\\ \sf\implies x = 50$

Thus , the age of A is 50 years and the age of B is 20 years