the ages of A and B are in the ratio 8 : 3 . after 6 years hence their

1.	the ages of A and B are in the ratio 8 : 3 . after 6 years hence their ages will be in the ratio 9:4 find their present ages ?
Answer» GIVEN : Ages of A and B are in the ratio $\rm \: 8:3$ After $\rm\red {6 \: years}$ , their ages will be in the ratio $\rm \: 9:4$ To Find : Their present ages. Calculation : Let, The present age of A be 8x The present age of B be 3x $\underline{ \bf {After \: 6 \: years, }}$ A's age will be 8x + 6 B's age will be 3x + 6 $\dag$ According to the QUESTION, $\bullet \: \: \bf \dfrac{8x + 6}{3x + 6} \: = \dfrac{9}{4}$ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\longrightarrow \rm \: 4 \: (3x + 6) = 9 \: (8x + 6) \\ \\ \\ \longrightarrow \rm \: 12x + 24 = 27 - 54 \\ \\ \\ \longrightarrow \rm \: 5x = 30 \\ \\ \\ \longrightarrow \rm \: x = \cancel \dfrac{30}{5} \\ \\ \\ \longrightarrow \boxed {\frak{ \red{x = 6}}} \star$ HENCEFORTH, A's age will be $\rm \: 8x$ $\longrightarrow \rm 8 \times 6 \\ \\ \\ \longrightarrow \boxed{\rm { \pink{48 \: years}}} \star$ B's age will be $\rm \: 3x$ $\longrightarrow \rm 3 \times 6 \\ \\ \\ \longrightarrow \boxed{\rm { \purple{18 \: years}}} \star$ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ Therefore, A's present age = $\bf\pink {48 \: years }$ B's present age = $\bf\purple {18 \: years}$

the ages of A and B are in the ratio 8 : 3 . after 6 years hence their ages will be in the ratio 9:4 find their present ages ?

Answer»

GIVEN :

Ages of A and B are in the ratio $\rm \: 8:3$

After $\rm\red {6 \: years}$ , their ages will be in the ratio $\rm \: 9:4$

To Find :

Their present ages.

Calculation :

Let,

The present age of A be 8x
The present age of B be 3x

$\underline{ \bf {After \: 6 \: years, }}$

A's age will be 8x + 6
B's age will be 3x + 6

$\dag$ According to the QUESTION,

$\bullet \: \: \bf \dfrac{8x + 6}{3x + 6} \: = \dfrac{9}{4}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\longrightarrow \rm \: 4 \: (3x + 6) = 9 \: (8x + 6) \\ \\ \\ \longrightarrow \rm \: 12x + 24 = 27 - 54 \\ \\ \\ \longrightarrow \rm \: 5x = 30 \\ \\ \\ \longrightarrow \rm \: x = \cancel \dfrac{30}{5} \\ \\ \\ \longrightarrow \boxed {\frak{ \red{x = 6}}} \star$