Question

the age of sunita and Sumatra is in the ratio of 5:3 After 6 years there age will be in the ratio of 7:5 what is the present age of sunita​

Answer 1

Given :

The age of sunita and Sumatra is in the ratio of 5:3 After 6 years there age will be in the ratio of 7:5 what is the present age of sunita

To find :

What is the present age of sunita

Solution :

Let present age of Sunita be 5x and Sumatra be 3x

According to the given condition

After 6 years

$\implies\sf \frac{5x+6}{3x+6}=\frac{7}{5} \\ \\ \implies\sf 5(5x+6)=7(3x+6) \\ \\ \implies\sf 25x+30=21x+42 \\ \\ \implies\sf 25x+21x=42-30 \\ \\ \implies\sf 4x=12 \\ \\ \implies\sf x=\frac{12}{4}=3$

${\boxed{\bf{x=3}}}$

Putting the value of x

${\boxed{\bf{Present\:age\:of\:Sunita=5x=15yrs}}}$

${\boxed{\bf{Present\:age\:of\:Sumatra=3x=9yrs}}}$

Verification :

$\implies\sf \frac{5x+6}{3x+6}=\frac{7}{5}$

LHS

$\implies\sf \large\frac{5x+6}{3x+6}$

Putting the value of x = 3

$\implies\sf \large\frac{5\times{3}+6}{3\times{3}+6}=\large\frac{21}{15}=\large\frac{7}{5}$ =RHS verified

Answer 2

GiVeN :-

• Ratio of Age of Sunita and Sumatra = 5:3

• Ratio of their ages after 6 years = 7:5

To FiNd :-

• Present age of Sunita

SoLuTiOn :-

Let the,

Present age of Sunita be x years

Present age of Sumatra be y years

Then,

According to 1st Condition :-

=> x : y = 5 : 3

$\implies \: \frac{x}{y} = \frac{5}{3} \\ \\ \implies \: x = \frac{5y}{3}$

Now,

After 6 years there age will be,

Sunita = (x + 6) years

Sumatra = ( y + 6) years

Then,

According to 2nd Condition,

=> (x+6) : (y+6) = 7 : 5

$\implies \: \frac{(x + 6)}{(y + 6)} = \frac{7}{5} \\ \\ \implies \: 5(x + 6) = 7(y + 6) \\ \\ \implies \: 5x + 30 = 7y + 42 \\ \\ \implies \: 5x - 7y = 12$

Now,

Put the above value of x in 5x - 7y = 12

Then,

We get,

$\implies \: 5 \times \frac{5y}{3} - 7y = 12 \\ \\ \implies \: \frac{25y}{3} - 7y = 12 \\ \\ \implies \: \frac{4y}{3} = 12 \\ \\ \implies \: y = \frac{12 \times 3}{4} = \frac{36}{4} = 9$

Now,

Put the value of y = 9 in first we get,

x = 5y/3

$x = \frac{5 \times 9}{3} = \frac{45}{3} = 15$

Hence,

• Age of Sunita = x = 15 years

• Age of Sumatra = y = 9 years