Question

Ratio of present age of A B and C is 4:6:7 respectively after 8 years ratio of age of a two age of B is 5:7 find the present age of c​

Answer 1

Answer :-

Therefore ,

• Present age of C is 56 years .

Step-by-step-Explaination :-

Correct Question :

Ratio of present age of A B and C is 4:6:7 respectively after 8 years the ratio of age of A and B is 5:7 find the present age of C .

Step 1 :

Understand it properly :-

See , here the ratio of A , B and C is given which is

4 : 6 : 7 respectively . Now , after 8 years , ratio of A and B is again given which is 5 : 7 . Hence , Find present age of C .

Now , this is basically from the chapter "Linear equation and inequation" . But , we have to solve it by Linear equation process as because this kind of Sum is not under Linear inequation . So, let's begin ..

Step 2 :

Assume the age :-

Let :

Now , from the present ratio (given) we have to assume them as age by inserting X at end .

• Let A's age be 4x
• Let B's age be 6x
• Let C's age be 7x

Hence 8 years ,

See , don't be confused " Hence 8 years " and " After 8 years " means the same . So, After 8 years all 3 of their ages will be +8 years .

• A's age after 8 years is (4x + 8 )
• B's age after 8 years is ( 6x + 8 )
• C's age after 8 years is ( 7x + 8 )

Step 3 :

Forming the equation :-

Now , Here is framing An equation , which needs to be solved to find X :-

Hence , the equation is :-

$\rm \: \dfrac{4x + 8}{6x + 8} = \dfrac{5}{7}$

Doing Cross-Multiplication of

• 7 and 4x + 8
• 5 and 6x + 8

$\implies \rm \:7 ({4x + 8} \: ) = 5({6x + 8} )$

Now , opening Brackets ,

$\implies \rm \:28x +56\: = 30x + 40$

Now , Bringing Both X ( Variable) one side and Constant another side . So, Sign changes

$\implies \rm \:56 - 40 = 30x - 28x$

$\implies \rm \:16 = 2 x$

Now , solving for X ,

$\implies \rm \: \cancel \dfrac{16}{2} = x$

$\implies \boxed{ \rm \: \bf 8 = x}$

Hence ,

• $\rm \: A's \: present \: age \: is \: {\bf4x} \longrightarrow4 \times 8 = \bf 32 \: years$
• $\rm \: B's \: present \: age \: is \: {\bf6x} \longrightarrow6\times 8 = \bf 48 \: years$
• $\rm \: C's \: present \: age \: is \: {\bf7x} \longrightarrow7\times 8 = \bf 56\: years$

Therefore ,

$\rm \therefore \: C's \: present \: age \: is \: {\bf7x} \longrightarrow7\times 8 = \bf 56\: years$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬