Question

Jorksheel 2
The present ages of A and B are in the ratio 7:5. Ten years later, their ages will
be in the ratio 9:7. Find their present ages.
EMT​

Answer 1

let the present age of A be 7x and B be 5x

Step-by-step explanation:

A.T.Q,

A:B = 7x : 5x

10 years later,

A's age= 7x + 10

B's age = 5x+10

Now, 7x + 10 / 5x + 10 = 9/7

7(7x+10) = 9(5x+10)

49x + 70 = 45x + 90

49x - 45x = 90-70

4x = 20

x= 20/4

x = 5

therefore, present age of A is 35 years

and the present age of B is 25 years

Answer 2

Given :

• Present Ages of A and B are in the ratio 7:5 .
• After 10 years their ages will be in the ratio 9:7 .

To Find :

• Present Ages of A and B .

Solution :

$\longmapsto\tt{Let\:Present\:age\:of\:A\:be=7x}$

$\longmapsto\tt{Let\:Present\:age\:of\:B\:be=5x}$

After 10 years :

$\longmapsto\tt{Age\:of\:A=7x+10}$

$\longmapsto\tt{Age\:of\:B=5x+10}$

A.T.Q :

$\longmapsto\tt{\dfrac{7x+10}{5x+10}=\dfrac{9}{7}}$

$\longmapsto\tt{7(7x+10)=9(5x+10)}$

$\longmapsto\tt{49x+70=45x+90}$

$\longmapsto\tt{49x-45x=90-70}$

$\longmapsto\tt{4x=20}$

$\longmapsto\tt{x=\cancel\dfrac{20}{4}}$

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

Value of x is 5 .

Therefore :

$\longmapsto\tt{Present\:Age\:of\:A=7(5)}$

$\longmapsto\tt\bf{35\:yrs}$

$\longmapsto\tt{Present\:Age\:of\:B=5(5)}$

$\longmapsto\tt\bf{25\:yrs}$