Question

five time the age of sita is 10 years more than four time the age of gita . fund their ages if their product of ages is 30​

Answer 1

Answer:

The age of Sita is 6 and the age of Gita is 5.

Step-by-step explanation:

Let the age  of Sita be $x$ and the age of Gita be $y$

Given that 5 times the age of Sita is 10 years that 4 times the age of Gita. Expressing the same as an equation, we get,

$5x=4y+10$

Also, the product of their ages is 30. Thus

$x\times y=30$

So,

$y=\frac{30}{x}$

Substitute for $y$ in the first equation,

$5x=4\times \frac{30}{x} +10$

Now we can solve for $x$.

.$5x=\dfrac{120}{x}+10\\\\5x=\dfrac{120+10x}{x} \\\\5x^2=120+10x\\\\x^2=24+2x\\\\x^2-2x-24=0$

Factorizing the above equation, we get,

$(x-6)(x+4)=0\\\implies x=6,-4$

Since age cannot be negative, we can take the value of $x$ as 6.

So the age of Sita is 6 and the age of Gita is 5.

Answer 2

Given :

Five time the age of sita is 10 years more than four time the age of gita .

product of their ages is 30.

Let Age of Sita be y yrs

and, Age of Gita be x yrs

Then, Equations are :

➻ 5y = 4x + 10 _____(1)

➻ xy = 30

⇒ x = 30/y

then, Substituting x = 30/y , we get

⇒ 5y = 4(30/y) + 10

⇒ 5y = (120y + 10y)/y

⇒ 5y² - 10y - 120 = 0

⇒ y² - 2y - 60 = 0

⇒ (y - 6)(y + 4) = 0

Since, Age can't be in Negative. y = 6

then,

x = 30/6

⇒ x = 5

FINAL ANSWER :

Age of Sita is 6 years

Age of Gita is 5 years