Question

the ages of simmy and Jimmy are in the ratio 6:8 five years from now the ratio of their ages will be 4:5 find their present ages​

Answer 1

Given :

• Present Ages of Simmy and Jimmy are in the ratio 6:8 .
• Five years from now the ratio of their ages will be 4:5 .

To Find :

• Present Ages .

Solution :

$\longmapsto\tt{Let\:Present\:Age\:of\:Simmy\:be=6x}$

$\longmapsto\tt{Let\:Present\:Age\:of\:Jimmy\:be=8x}$

After 5 years :

$\longmapsto\tt{Age\:of\:Simmy=6x+5}$

$\longmapsto\tt{Age\:of\:Jimmy=8x+5}$

A.T.Q :

$\longmapsto\tt{\dfrac{6x+5}{8x+5}=\dfrac{4}{5}}$

$\longmapsto\tt{5(6x+5)=4(8x+5)}$

$\longmapsto\tt{30x+25=32x+20}$

$\longmapsto\tt{30x-32x=20-25}$

$\longmapsto\tt{-2x=-5}$

$\longmapsto\tt\bf{x=\dfrac{5}{2}}$

Value of x is 5/2 .

Therefore :

$\longmapsto\tt{Present\:Age\:of\:Simmy={\not{6}}\times\dfrac{5}{{\not{2}}}}$

$\longmapsto\tt{3\times{5}}$

$\longmapsto\tt\bf{15\:yrs}$

$\longmapsto\tt{Present\:Age\:of\:Jimmy={\not{8}}\times\dfrac{5}{{\not{2}}}}$

$\longmapsto\tt{4\times{5}}$

$\longmapsto\tt\bf{20\:yrs}$

Answer 2

Given :-

The  ages of Simmy and Jimmy are in the ratio 6:8 five years from now the ratio of their ages will be 4:5

To Find :-

Present ages

Solution :-

Let the present age of Simmy be 6y and Jimmy be 8y

After 5 years

6y + 5/8y + 5 = 4/5

• Need to do cross multiplication

5(6y + 5) = 4(8y + 5)

$\sf (5 \times 6y) + (5\times 5)=(4 \times 8y)+(4 \times 5)$

30y + 25 = 32y + 20

32y - 30y = 25 - 20

2y = 5

y = 5/2

Or,

y = 5

Age of simmy

$\sf 6 \times 2.5$

15 years

Age of Jimmy

$\sf 8 \times 2.5$

20 years