the present age of the brother n sister are in the ratio of the 4 is to 5 before three of the ratio of their it was 3 is to 4 find their present age
Answers
Answer:
Present age of brother = 12 years
Present age of sister = 15 years
\underline{ \underline{ \Large \pmb{\sf { {Step-by-step \: solution:}} }} }
Step−by−stepsolution:
Step−by−stepsolution:
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} }⟶
5x−3
4x−3
=
4
3
By using cross multiplication method.
\longrightarrow \sf { 4(4x-3) = 3(5x - 3) }⟶4(4x−3)=3(5x−3)
By distributive property,
\longrightarrow \sf { 4(4x) - 4(3)= 3(5x) + 3( - 3) }⟶4(4x)−4(3)=3(5x)+3(−3)
Performing multiplication.
\longrightarrow \sf { 16x - 12= 15x -9 }⟶16x−12=15x−9
Transposing like terms.
\longrightarrow \sf { 16x - 15x = -9 + 12 }⟶16x−15x=−9+12
Performing addition & subtraction.
\longrightarrow \sf { x = 3}⟶x=3
Henceforth,
→ Present age of brother = 4x years
→ Brother's age = 4(3) years
\begin{gathered}\to \bigstar \: \boxed{\sf \purple {Brother's \: age =12 \: years }} \\ \end{gathered}
→★
Brother
′
sage=12years
And,
→ Present age of sister = 5x years
→ Sister's age = 5(3) years
\begin{gathered}\to \bigstar \: \boxed{\sf \purple {Brother's \: age =15 \: years }} \\ \end{gathered}
→★
Brother
′
sage=15years
Step-by-step explanation:
let the present age ratio of brother and sister be 4x and 5x
before 3 years
age of brother = 4x-3
age of sister = 5x-3
their ratio = 3:4
4x-3/5x-3 = 3/4
cross multiplication
4(4x-3)=3(5x-3)
16x-12=15x-9
16x-15x=-9+12
x=3
hence x=3
age of brother = 4(3)-3 = 12-3 = 9
age of sister = 5(3)-3 = 15-3 = 12
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