Question

6. Ten years ago, A's age was half of B's age. If
the ratio of their present ages is 3 : 4, what
will be the sum of their present ages?​

Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

Assumption :-

Present age of A be 3p

Present age of B be 4p

${\boxed{\sf\:{Ten\;years\;ago}}}$

A age should be 3p - 10

B age should be 4p - 10

${\boxed{\sf\:{A\;age\;was\;half\;of\;B \;age}}}$

Situation should be like this :-

$\tt{\rightarrow (3p-10)=\dfrac{1}{2}(4p-10)}$

2(3p - 10) = 4p - 10

6p - 20 = 4p - 10

2p = 10

$\tt{\rightarrow p=\dfrac{10}{2}}$

p = 5

${\boxed{\sf\:{Present\;age\;of\;A}}}$

= 3p

= 15

${\boxed{\sf\:{Present\;age\;of\;B}}}$

= 4p

= 20

${\boxed{\sf\:{Sum\;Present\;age}}}$

= 20 + 15

= 35

Answer 2

Answer:

Ten years a go,

$A's \: age = \frac{B's \: age}{2} \: \: ......... \: (1) \\ B's \: age = 2 \: A's \: age \: ........(2)$

Present age of,

A = 3x .........(3)

B= 4x ..........(4)

Age before 10 years from now,

A= 3x -10 ...........(5)

B= 4x -10 ..........(6)

now,

equating equation (1) and equation (5) or question (2) and equation (6)

the value of x will be same ,

$3x - 10 = \frac{B's \: age \: before \: 10 \: years}{2} \\ = > 3x - 10 = \frac{4x - 10}{2} \\ = > 6x - 20 = 4x - 10 \\ = > 6x - 4x = 20 - 10 \\ = > 2x = 10 \\ = > x = 5$

now on putting the vale of x on equation (3) and (4) we get,

A's age = 3x

=3 X 5

=15 years old

B's age = 4x

= 4 X 5

=20 years old

Hence, the present age of A and B is 15 and 20 years old respectively.

Now sum of there present age is

20+15

=35