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Answers
Step-by-step explanation:
Answer:
In 15 years, the ratio of A and B's ages will be 6:7.
Step-by-step explanation:
A's present age to B's present age = 7 : 9
Ratio of their ages 12 years ago = 3 : 5
When would the ratio of their ages be 6 : 7
Let present ages of A and B be x and y respectively.
So, x : y = 7 : 9
\sf{\longrightarrow} \: \dfrac{x}{y} = \dfrac{7}{9}⟶
y
x
=
9
7
\sf{\longrightarrow} \:9x = 7y⟶9x=7y
\sf{\longrightarrow} \:x = \dfrac{7y}{9} \: - - - - (Eq.1)⟶x=
9
7y
−−−−(Eq.1)
___________________
Ages 12 years ago -
A's age = (x - 12)
B's age = (y - 12)
So, (x - 12) : (y - 12) = 3 : 5
\sf{\longrightarrow} \: (x - 12) : (y - 12) = 3 : 5⟶(x−12):(y−12)=3:5
\sf{\longrightarrow} \: \dfrac{ (x - 12)}{(y - 12) }= \dfrac{3}{5}⟶
(y−12)
(x−12)
=
5
3
\sf{\longrightarrow} \:5(x - 12) = 3(y - 12)⟶5(x−12)=3(y−12)
\sf{\longrightarrow} \:5x - 60= 3y - 36⟶5x−60=3y−36
\sf{\longrightarrow} \:5x - 3y= - 36 + 60⟶5x−3y=−36+60
\sf{\longrightarrow} \:5x - 3y = 24 \: - - - - (Eq.2)⟶5x−3y=24−−−−(Eq.2)
___________________
Substitute Equation 1 in Equation 2,
\sf{\longrightarrow} \:5\left( \dfrac{7y}{9}\right) - 3y = 24⟶5(
9
7y
)−3y=24
\sf{\longrightarrow} \: \dfrac{35y}{9} - 3y = 24⟶
9
35y
−3y=24
\sf{\longrightarrow} \: \dfrac{35y - 27y}{9} = 24⟶
9
35y−27y
=24
\sf{\longrightarrow} \:8y = 24 \times 9⟶8y=24×9
\sf{\longrightarrow} \:8y = 216⟶8y=216
\sf{\longrightarrow} \:y = \dfrac{216}{8}⟶y=
8
216
\sf{\longrightarrow} \:y = 27⟶y=27
___________________
Put the value of y in equation 1,
\sf{\longrightarrow} \:x = \dfrac{7(27)}{9}⟶x=
9
7(27)
\sf{\longrightarrow} \:x = \dfrac{189}{9} = 21⟶x=
9
189
=21
\sf{\longrightarrow} \:x = 21⟶x=21
Present ages of A and B is 21 and 27 years.
___________________
Let after z years, ratio of A and B be 6 : 7.
\sf{\longrightarrow} \: \dfrac{(21 + z)}{(27 + z)} = \dfrac{6}{7}⟶
(27+z)
(21+z)
=
7
6
\sf{\longrightarrow} \:7(21 + z) = 6(27 + z)⟶7(21+z)=6(27+z)
\sf{\longrightarrow} \:147 + 7z = 162 + 6z⟶147+7z=162+6z
\sf{\longrightarrow} \:7z - 6z = 162 - 147⟶7z−6z=162−147
\sf{\longrightarrow} \:z = 15⟶z=15
After 15 years, ages of A and B will be in ratio 6 : 7.
Therefore, In 15 years, the ratio of A and B's ages will be 6:7.