Question

the difference between the ages of two sisters is 3 years . six years hence the ratio of their ages will be 7 : 6 . what is the age of each sister today ?​

Answer 1

Answer:

$\large\bold\red{12\:yrs\:and\:15\:yrs}$

Step-by-step explanation:

Let's assume that,

• First Sister = S1
• Second Sister = S2

Now,

Let's take ,

The present age of S1 = x yrs.

Therefore,

The present age of S2 = (x+3) yrs.

After 6 yrs,

Age of S1 = (x+6) yrs.

And,

Age of S2 = (x+9) yrs.

Now,

According to question,

We get,

$= > \frac{x + 9}{x + 6} = \frac{7}{6} \\ \\ = > 6(x + 9) = 7(x + 6) \\ \\ = > 6x + 54 = 7x + 42 \\ \\ = > 7x - 6x = 54 - 42 \\ \\ = > x = 12$

Therefore,

$= > x + 3 = 15$

Hence,

Present age of S1 = 12 yrs.

And,

Present age of S2 = 15 yrs.

Answer 2

Answer:

Age of one sister: 15 years.

Age of another sister:12 years.

$\huge\underline\mathfrak\blue{Solution..}$

Let the age of one sister be "X" years

Let the age of another sister be "Y" years.

First equation is:

X-Y =3

So, X =Y +3..............(i)

Second equation is:

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

or, (X+6)/(Y+6)=7/6

or, 6(X+6)=7(Y+6)

or, 6X+36=7Y+42

or, 6X =7Y+42-36

or, 6X =7Y+6

So, X =(7Y+6)/6.............(ii)

Then by substituting the value of (i) equation we get,

Y+3=(7Y+6)/6

or, (7Y+6)/6=Y+3

or, 7Y+6=6(Y+3)

or, 7Y+6=6Y+18

or, 7Y-6Y=18-6

So, Y =12⭐⭐⭐

So, Second sister's present

age is: 12 years.

By substituting the value of Y into the (i) equation we get,

X =12+3

So, X =15⭐⭐⭐

So,First sister's age is :15

years.

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