Question

the ages of reena and meena are in the ratio 3:4 .Eight years from now the ratio of their ages will be 5:6.Find their present ages?

Answer 1

Answer:

The present ages of Reena and Meena are 12 years and 16 years respectively.

Step-by-step explanation:

Given :

Present age Ratio = 3 : 4

Ratio of ages after 8 years = 5 : 6

To find :

Their present ages

Solution :

Let the present ages be -

• Reena as 3y
• Meena as 4y

Ages after 8 years -

• Reena = (3y + 8)
• Meena = (4y + 8)

According to the question,

Reena and Meena after 8 years have their age Ratio as 5 : 6

$\boxed{\tt{\frac{3y + 8}{4y + 8} = \frac{5}{6}}}$

$\tt{\longrightarrow} \: \dfrac{3y + 8}{4y + 8} = \dfrac{5}{6} \\ \\ \tt{\longrightarrow} \: 6(3y + 8) = 5(4y + 8) \\ \\ \tt{\longrightarrow} \: 18y + 48 = 20y + 40 \\ \\ \tt{\longrightarrow} \: 20y - 18y = 48 - 40 \\ \\ \tt{\longrightarrow} \: 2y = 8 \\ \\ \tt{\longrightarrow} \: y = \dfrac{8}{2} \\ \\ \tt{\longrightarrow} \: y = 4$

$\rule{300}{0.5}$

★ Reena's present age -

$\tt{\longrightarrow} \: 3(4)\\ \\ \tt{\longrightarrow} \: 12$

Reena is 12 years old.

$\rule{300}{0.5}$

★ Meena's present age -

$\tt{\longrightarrow} \: 4(4) \\ \\ \tt{\longrightarrow} \: 16$

Meena is 16 years old.

$\therefore$ The present ages of Reena and Meena are 12 years and 16 years respectively.

Answer 2

Step-by-step explanation:

Given -

Present age 3 : 4

Ratio after 8 years = 5 : 6

To find -

Their present ages

Solution -

Consider the present ages as

• Reena as 3a
• Meena as 4a

$\sf{\implies} \frac{3a + 8}{4a + 8} = \frac{5}{6} \\ \\ \sf{\implies}6(3a + 8) = 5(4a + 8) \\ \\ \sf{\implies}18a + 48 = 20a + 40 \\ \\ \sf{\implies}48 - 40 = 20a - 18a \\ \\ \sf{\implies}8 = 2a \\ \\ \sf{\implies}a = 4$

Reena = 3a = 3 × 4 = 12

Meena = 4a = 4 × 4 = 16

$\therefore$ Reena is 12 years old and Meena is 16 years old.