The ratio of ages of (in years)of A and B,9 years ago,was 23:12.The ratio of their ages after 15 years will be 35:24.What is the ratio of present ages of A and B?
Answers
5 : 3
explanation,
9 years ago,
23 : 12
now,
A: B
15 years after,
35 : 25
now,
total gap is 12 parts and now add the years difference i.e., 9+15=24
so, 12=24 --> 1 part = 2 years
so, 9 years ago, A's ages was 23×2= 46 and B's age was 12×2=24
therefore the answer will be 46+9 : 24+9
i.e., 55:33 and the answer will be 5:3
The ratio of ages (in years) of A and B 9 years ago, was 23:12. The ratio of their ages after 15 years will be 35:24. What is the ratio of present ages of A and B?
\sf Answer :Answer:
Let the Age of A be 23x and of B be 12x 9 years ago from Present Age.
\underline{\bigstar\:\textsf{According to the given Question :}}
★According to the given Question :
\begin{gathered}:\implies\sf \dfrac{A+9+15}{B+9+15}=\dfrac{35}{24}\\\\\\:\implies\sf \dfrac{23x+9+15}{12x+9+15}=\dfrac{35}{24}\\\\\\:\implies\sf \dfrac{23x+24}{12x+24}=\dfrac{35}{24}\\\\\\:\implies\sf \dfrac{23x+24}{12(x+2)}=\dfrac{35}{24}\\\\\\:\implies\sf \dfrac{23x+24}{x+2}=\dfrac{35}{2}\\\\\\:\implies\sf (23x + 24) \times 2 = 35 \times (x + 2)\\\\\\:\implies\sf 46x + 48 = 35x + 70\\\\\\:\implies\sf 46x - 35x = 70 - 48\\\\\\:\implies\sf 11x = 22\\\\\\:\implies\sf x = \dfrac{22}{11}\\\\\\:\implies\sf x = 2\end{gathered}
:⟹
B+9+15
A+9+15
=
24
35
:⟹
12x+9+15
23x+9+15
=
24
35
:⟹
12x+24
23x+24
=
24
35
:⟹
12(x+2)
23x+24
=
24
35
:⟹
x+2
23x+24
=
2
35
:⟹(23x+24)×2=35×(x+2)
:⟹46x+48=35x+70
:⟹46x−35x=70−48
:⟹11x=22
:⟹x=
11
22
:⟹x=2
\rule{180}{1.5}
\underline{\bigstar\:\textsf{Required ratio of Present Age of A \& B:}}
★Required ratio of Present Age of A & B:
\begin{gathered}\dashrightarrow\sf \:\:\dfrac{A}{B}=\dfrac{23x+9}{12x+9}\\\\\\\dashrightarrow\sf \:\: \dfrac{A}{B}=\dfrac{23(2)+9}{12(2)+9}\\\\\\\dashrightarrow\sf \:\: \dfrac{A}{B}=\dfrac{46+9}{24+9}\\\\\\\dashrightarrow\sf \:\: \dfrac{A}{B}=\dfrac{55}{33}\\\\\\\dashrightarrow\sf \:\: \dfrac{A}{B}=\dfrac{5}{3}\\\\\\\dashrightarrow \: \:\underline{\boxed{\sf A:B = 5:3}}\end{gathered}
⇢
B
A
=
12x+9
23x+9
⇢
B
A
=
12(2)+9
23(2)+9
⇢
B
A
=
24+9
46+9
⇢
B
A
=
33
55
⇢
B
A
=
3
5
⇢
A:B=5:3