Question

The Ages Of Teena And Meena Are In The Ratio 3:4. Six Years From Now , The Ratio Of Their Ages Will Be 5:6. Find Their Present Ages.

Answer 1

Answer:

$\large{\underline{\boxed{\sf Teena's \: age = 9 \: years}}}$

$\large{\underline{\boxed{\sf Meena's \: age = 12 \: years }}}$

Step-by-step explanation:

Let the present age of Teena and Meena be 3x and 4x respectively.

It is given that, after 6 years their ratio will be 5:6.

But, after 6 years

• Teena's age = 3x + 6
• Meena's age = 4x + 6

So, equation formed :

★ $\boxed{\tt \dfrac{3x + 6}{4x + 6}= \dfrac{5}{6}}$

On solving the above equation,

$\implies \tt \frac{3x + 6}{4x + 6} = \frac{5}{6} \\ \\ \bf on \: cross - multipying : \\ \\ \implies \tt 6(3x + 6) = 5(4x + 6) \\ \\ \implies \tt 18x + 36 = 20x + 30 \\ \\ \implies \tt 18x - 20x = 30 - 36 \\ \\ \implies \tt - 2x = - 6 \\ \\ \implies \tt x = \frac{ - 6}{ - 2} \\ \\ \implies \tt x = 3$

Therefore,

• Teena's age = 3x = 3 * 3 = 9 years
• Meena's age = 4x = 4 * 3 = 12 years.

$\rule{300}{2}$

Hence, the present age of Teena is 9 years and present age of Meena is 12 years.

Answer 2

Answer:

Age of Teena = 9 years

Age of Meena = 12 years

Step-by-step explanation:

given that,

The Ages Of Teena And Meena Are In The Ratio 3:4

let the common ratio of their ages be x

so,

age of Teena = 3x

age of Meena = 4x

given

Six Years From Now , The Ratio Of Their Ages Will Be 5:6.

so

ATQ,

(3x + 6)/(4x + 6) = 5/6

cross multiplication

6(3x + 6)=5(4x + 6)

18x + 36=20x + 30

18x − 20x = 30 − 36

−2x=−6

x = -6/-2

x = 3

so,

age of Teena

= 3x

=3(3)

= 9 years

age of Meena = 4x

= 4(3)

= 12 years

so,

Age of Teena = 9 years

Age of Meena = 12 years