Question

The present age of brother and sister is in the ratio 4:5. Before three years the ratio of
their age was 3: 4. Find their present age.

Answer 1

$\underline{ \underline{ \Large \pmb{\sf { {Answer:}} }} }$

• Present age of brother = 12 years
• Present age of sister = 15 years

$\underline{ \underline{ \Large \pmb{\sf { {Step-by-step \: solution:}} }} }$

Let the present age of brother and sister be 4x and 5x years respectively.

Before three years :-

• Brother's age = 4x - 3
• Sister's age = 5x - 3

In the question, it is stated that before three years the ratio of their age was 3: 4. So, according to the question :

$\longrightarrow \sf { \dfrac{4x - 3}{5x-3} = \dfrac{3}{4} }$

• By using cross multiplication method.

$\longrightarrow \sf { 4(4x-3) = 3(5x - 3) }$

• By distributive property,

$\longrightarrow \sf { 4(4x) - 4(3)= 3(5x) + 3( - 3) }$

• Performing multiplication.

$\longrightarrow \sf { 16x - 12= 15x -9 }$

• Transposing like terms.

$\longrightarrow \sf { 16x - 15x = -9 + 12 }$

• Performing addition & subtraction.

$\longrightarrow \sf { x = 3}$

Henceforth,

→ Present age of brother = 4x years

→ Brother's age = 4(3) years

$\to \bigstar \: \boxed{\sf \purple {Brother's \: age =12 \: years }}$

And,

→ Present age of sister = 5x years

→ Sister's age = 5(3) years

$\to \bigstar \: \boxed{\sf \purple {Brother's \: age =15 \: years }}$

⠀⠀⠀⠀⠀_____________

$\underline{ \underline{ \Large \pmb{\sf { {Verification:}} }} }$

In the question, it is stated that the present ages of them are in ration 4:5 and before three years the ratio of their age was 3:4. So,

$\longrightarrow \sf { \dfrac{4x - 3}{5x-3} = \dfrac{3}{4} }$

LHS:

$\longrightarrow \sf { \dfrac{4x - 3}{5x-3} }$

$\longrightarrow \sf { \dfrac{4(3) - 3}{5(3)-3} }$

$\longrightarrow \sf { \dfrac{12- 3}{15-3} }$

$\longrightarrow \sf { \dfrac{9}{12} }$

Reducing it to lowest terms.

$\longrightarrow \sf { \dfrac{3}{4} }$

RHS:

$\longrightarrow \sf { \dfrac{3}{4} }$

Therefore, LHS = RHS.

Hence, verified!!

Answer 2

Given :

• The present age of brother and sister is in the ratio 4:5.
• Before three years the ratio of their age was 3: 4.

To Find :

• Their Present Ages

Solution :

⟶ Let the Present Age of Brother be 4x

⟶ Let the Present Age of Sister be 5x

Before 3 Years :

⟶ The Present Age of Brother = 4x - 3

⟶ The Present Age of Brother = 5x - 3

⠀

According to the Question :

➟ 4x - 3 / 5x - 3 = 3/4

➟ 4 (4x - 3) = 3 (5x - 3)

➟ 16x - 12 = 15x - 9

➟ 16x - 15x = 12 - 9

➟ x = 3

________________

Therefore :

• Present age of Brother = 4x
• Present age of Brother = 4 × 3
• Present age of Brother = 12 years

• Present age of Sister = 5x
• Present age of Sister = 5 × 3
• Present age of Sister = 15years

________________