Question

Sohe the following.
1. The ratio of the present ages of Radha and Meera is 2: 5. Six years hence, the ratio of their
ages will be 1:2. Find their present ages.​

Answer 1

Answer:

The present age of Radha is 12 years

The present age of Meera is 30 years

Step-by-step explanation:

Let,

The present age of Radha = 2x

The present age of Meera = 5x

Six years hence,

The age of Radha = 2x + 6

The age of Meera = 5x + 6

Also,

The ratio of their ages will be 1 : 2

So,

⇒ $\frac{2x \: + \: 6}{5x \: + \: 6} \: = \: \frac{1}{2}$

⇒ 2 (2x + 6) = 1 (5x + 6)

⇒ 4x + 12 = 5x + 6

⇒ 4x - 5x = 6 - 12

⇒ - 1x = - 6

⇒ x = 6

____________________________

★ Value of 2x :

⇒ 2 (6)

⇒ 12

____________________________

★ Value of 5x :

⇒ 5 (6)

⇒ 30

Therefore,

The present age of Radha is 12 years

The present age of Meera is 30 years

Answer 2

Given :

• Ratio of the present ages of Radha and Meera =2:5
• Six years hence, the ratio of their ages will be 1:2.

To Find :

• The present ages of Radha and Meera.

Solution :-

Let the present ages of Radha and Meera be 2x years and 5x years.

Six years hence,

• Age of Radha = (2x+6) years
• Age of Meera = (5x+6) years

According to question ,

$: \implies {\sf {\dfrac {2x+6}{5x+6} =\dfrac {1}{2}}}\\ \\ : \implies {\sf {2 (2x+6) = 1 (5x+6)}}\\ \\ : \implies {\sf {4x+12=5x+6}}\\ \\ : \implies {\sf {12-6=5x-4x}}\\ \\ : \implies {\sf {6=x}}\\ \\ : \implies {\boxed {\tt {x=6}}}$

$\therefore{\underline{\sf{The\: present\: age \:of\: Radha\: is\: (2\times 6) \:years} = \bf{12\:years}.}}$

$\therefore{\underline {\sf {The\: present\:age\:of\:Meera \:is \:(5\times 6)\:years}= \bf{30 \:years}.}}$