Question

The age of A is five years more than that of B. 5 years ago the ratio of their ages was 3:2 . Find their present ages​

Answer 1

✬ A's age = 20 Years ✬

✬ B's age = 15 Years ✬

Step-by-step explanation:

Given:

• Age of A is five years more that B's age.
• 5 years ago the ratio of their ages was 3:2.

To Find:

• What is their present ages ?

Solution: Let the age of B be x years. Therefore

➼ A's age = 5 years more than B's age.

➼ A's age = (x + 5) years.

Now, 5 years ago their ages was:-

• B's age = (x – 5) Years
• A's age = (x + 5 – 5) = (x) Years.

A/q

• Five years age the ratio of their ages will 3 : 2

$\implies{\rm }$ (A's age) : (B's age) = 3 : 2

$\implies{\rm }$ (x) / (x – 5) = 3/2

$\implies{\rm }$ 2(x) = 3(x – 5)

$\implies{\rm }$ 2x = 3x – 15

$\implies{\rm }$ 2x – 3x = – 15

$\implies{\rm }$ – x = – 15

$\implies{\rm }$ x = 15

Hence,

➟ Age of B = x = 15 years

➟ Age of A = (x + 5) = 15+5 = 20 years

Answer 2

GIVEN:

• The age of A is five years more than that of B
• 5 years ago the ratio of their ages was 3:2

TO FIND:

• What are their presence ages ?

SOLUTION:

Let the age of A be 'p' years and that of B be 'q' years

Case:- ❶

☛ The age of A is five years more than that of B

$\bf{\dashrightarrow p = q + 5....1) }$

Case:- ❷

☛ 5 years ago the ratio of their ages was 3:2

• A's age = (p - 5) years
• B's age = (q - 5) years

According to question:-

$\rm{\dashrightarrow \dfrac{ p - 5}{q - 5} = \dfrac{3}{2}}$

$\rm{\dashrightarrow 2(p-5) = 3(q-5) }$

$\rm{\dashrightarrow 2p - 10 = 3q - 15 }$

$\rm{\dashrightarrow 2p - 3q = -15 + 10}$

$\rm{\dashrightarrow 2p - 3q = -5 }$

Put the value of 'p' from equation 1)

$\rm{\dashrightarrow 2(q+5) - 3q = -5 }$

$\rm{\dashrightarrow 2q + 10 - 3q = -5 }$

$\rm{\dashrightarrow -q = -5 -10}$

$\rm{\dashrightarrow \cancel{-} q = \cancel{-} 15 }$

$\bf{\dashrightarrow q = 15\: years }$

Put the value of 'q' in equation 1)

$\rm{\dashrightarrow p = 15 + 5 }$

$\bf{\dashrightarrow p = 20 \: years}$

• A's age = p = 20 years
• B's age = q = 15 years

❝ Hence, the present ages of A and B are 20 years and 15 years respectively. ❞

______________________