Question

the ratio between the present ages of a and b is 2 : 3 five years ago their age was 7 : 1 find the present ages of a and b​

Answer 1

Given :-

• The ratio between the present ages of a and b is 2 : 3 five years ago their age was 7 : 1.

To Find :-

• The present age of a and b = ?

Solution :-

• Let present age of a and b be 2x and 3x respectively.

★ 5 years ago :-

• Age of a = 2x - 5
• Age of b = 3x - 5

★ According to Question now :-

➻ 2x - 5 ÷ 3x - 5 = 7 ÷ 1

By Cross multiplication we get :-

➻ (2x - 5) 1 = 7 (3x - 5)

➻ 2x - 5 = 21x - 35

Combining like terms :-

➻ -5 + 35 = 21x - 2x

➻ 30 = 19x

➻ x = 30 ÷ 19

➻ x ≈ 1.5

Hence,

• Present age of a = 2x = 2(1.5) = 3 years
• Present age of b = 3x = 3(1.5) = 4.5 years

Answer 2

★ Given Question ★

The ratio between the present ages of a and b is 2 : 3 five years ago their age was 7 : 1.Find the present ages of a and b.

★ Required Answer ★

Given:

• Ratio between the present ages of a and b is 2:3

• Five years ago their age was 7:1

To calculate :

• What is the present age of a and b?

Calculation:

As in the question we are given that the present ages of a and b is 2 : 3, so let's assume a's age as 2x and b's age as 3x.

So their ages before 5 years ago-

✤ 2x - 5 = a's age

✤ 3x - 5 = b's age

Now, also given that five years ago their age was 7 : 1 or 7/1.

Therefore, suitable equation formed:

$\sf { \implies \dfrac { 2x-5}{3x-5} = \dfrac{7}{1 } }$

$\sf { \implies 1(2x-5) = 7(3x-5) }$

$\sf { \implies 2x - 5 = 21x -35 }$

$\sf { \implies 2x - 21x = -35+5 }$

$\sf { \implies -19x = -30 }$

$\sf { \implies x = \dfrac{-30}{-19} }$

$\sf { \implies x = 1.5 }$$\purple { \bigstar }$

Therefore, present ages of 'a' and 'b' -:

✤ a's present age = 2x

$\qquad$ = $\sf { 2 \times 1.5}$

$\qquad$ = $\sf \red { 3years }$

✤ b's present age = 3x

$\qquad$ = $\sf { 3 \times 1.5}$

$\qquad$ = $\sf \red { 4.5 \: years }$

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