Question

the ages of A and B are in tatio 5:7. Four years from now the ratio of their ages will be 3:4. the present age of B is​

Answer 1

Given :

• Ages of A and B are in ratio 5:7.
• After 4 years their ages will be 3:4 .

To Find :

• Present age of B.

Solution :

$\longmapsto\tt{Let\:age\:of\:A=5x}$

$\longmapsto\tt{Let\:age\:of\:B=7x}$

After 4 years :

$\longmapsto\tt{Age\:of\:A=5x+4}$

$\longmapsto\tt{Age\:of\:B=7x+4}$

A.T.Q :

$\longmapsto\tt{\dfrac{5x+4}{7x+4}=\dfrac{3}{4}}$

$\longmapsto\tt{4(5x+4)=3(7x+4)}$

$\longmapsto\tt{20x+16=21x+12}$

$\longmapsto\tt{20x-21x=12-16}$

$\longmapsto\tt{-1x=-4}$

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

Value of x is 4..

Therefore :

$\longmapsto\tt{Present\:age\:of\:B=7(4)}$

$\longmapsto\tt\bold{28\:yrs.}$

So , The present age of B is 28 years..

Answer 2

Step-by-step explanation:

Q :

\longmapsto\tt{\dfrac{5x+4}{7x+4}=\dfrac{3}{4}}⟼

7x+4

5x+4

=

4

3

\longmapsto\tt{4(5x+4)=3(7x+4)}⟼4(5x+4)=3(7x+4)

\longmapsto\tt{20x+16=21x+12}⟼20x+16=21x+12

\longmapsto\tt{20x-21x=12-16}⟼20x−21x=12−16

\longmapsto\tt{-1x=-4}⟼−1x=−4

\longmapsto\tt\bold{x=4}⟼x=4

Value of x is 4..

Therefore :

\longmapsto\tt{Present\:age\:of\:B=7(4)}⟼PresentageofB=7(4)

\longmapsto\tt\bold{28\:yrs.}⟼28yrs.

So , The present age of B is 28 years