Question

The present age of surbhi and ramya are in the ratio 3:4. ten years from now the ratio of their ages will be 5:6 find their present ages


pls help me

Answer 1

Surbhi's age = 15 years

Ramya's age = 20 years

Step-by-step explanation:

★Given -

• The present age of Surbhi and Ramya are in the ratio 3:4.
• Ten years from now the ratio of their ages will be 5:6.

★To find -

• Their present ages.

★Solution -

Let the present ages of Surbhi and Ramya be 3x and 4x.

10 years later,

Surbhi's age = (3x + 10) years

Ramya's age = (4x + 10) years

Now, according to the second statement,

$\longmapsto \rm \dfrac{3x + 10}{4x + 10} = \dfrac{5}{6}$

$\longmapsto \rm 6{(3x + 10)}= {5(4x + 10)}$

$\longmapsto \rm 18x + 60 = 20x + 50$

$\longmapsto \rm 60 - 50= 20x - 18x$

$\longmapsto \rm 10 = 2x$

$\longmapsto \rm \dfrac{ \cancel{10}}{ \cancel2} = \large{x}$

$\longmapsto \rm\large \bf \orange{5 = x}$

Therefore, present age of Surbhi,

=> 3 × 5

=> 15 years

And age of Ramya,

=> 4 × 5

=> 20 years

Answer 2

Answer :-

• Surbhi's age = 15 years

• Ramya's age = 20 years

Explanation :-

$\longrightarrow$ The present age of Surbhi and ramya are in the ratio 3:4

$\longrightarrow$ Let the present age of Surbhi = $\sf 3 \: \: k$

$\longrightarrow$ and the present age of ramya = $\sf 4 \: \: k$

$\longrightarrow$ Now, As given in question,

$\longrightarrow$ After ten years from now age of Surbhi = $\sf 3 \: \: k + 10$

$\longrightarrow$ and After ten years from now age of Ramya = $\sf 4 \: \: k + 10$

$\longrightarrow$ And their ratio = 5:6 (given in question )

$\longrightarrow$ Hence, we get,

• $\sf \frac{3 \: \: k+10}{4 \: \: k+10} = \frac{5}{6}$

• Now, we can solve it very easily

• $\sf \frac{3 \: \: k+10}{4 \: \: k+10} = \frac{5}{6}$

• $\sf 6(3 \: \: k+10) = 5(4 \: \: k+10)$

• $\sf 18 \: \: k + 60 = 20 \: \: k + 50$

• $\sf 60 - 50 = 20 \: \: k - 18 \: \: k$

• $\sf 10 = 2 \: \: k$

• $\sf k = \frac{\cancel{10}^{\: \: 5}}{\cancel {2}}$

• $\sf \underline{ k = 5 }$

______________________

$\sf \longrightarrow$ Now, For Surbhi's age

= 3k

= 3(5)

= 15 years

______________________

$\sf \longrightarrow$ For Ramya's age

= 4k

= 4(5)

= 20 years

______________________

I hope it helps you ❤️✔️