Question

Six years ago, the age of Grace and Sima were in the ratio of 3:4. Nine years hence, there age will be in the ratio 6:7. Find there present age

Answer 1

Answer:

15 and 17 years.

Step-by-step explanation:

3x and 4x.

six years ago.

3x-6/ 4x- 6= 6/7

7(3x-6)= 6(4x-6).

21x - 42= 24x - 36.

3x = 42-36.

3x = 6

X = 6/3.

X= 2.

now ,

present age of grace = 3*2=6.

present age of sima = 4*2= 8.

and nine years hence now,

grace = 6+9.= 15.years

sima = 8+9 = 17 years

Answer 2

Answer:

Let the age of Grace and Sima be x and y respectively.

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☯ 6 years ago,

(x - 6)/(y - 6) = 3/4

4(x - 6) = 3(y - 6)

4x - 24 = 3y - 18

4x - 3y = 6

4x - 3y - 6 = 0........(Equation 1)

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☯ 9 years later,

(x + 9)/(y + 9) = 6/7

7(x + 9) = 6(y + 9)

7x + 63 = 6y + 54

7x - 6y + 9 = 0..........(Equation 2)

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Now,

★ 8x - 16y - 12 = 0........(multiplying equation 1 by 2)

So, By elimination method we get:

8x - 6y - 12 = 0

7x - 6y + 9 = 0

(+) (+)

____________

x - 21 = 0

x = 21 years

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Now, putting the value of x = 21 in equation (1) :

4x - 3y - 6 = 0

4(21) - 3y - 6 = 0

84 - 6 = 3y

78 = 3y

y = 78/3

y = 26 years

Therefore,

• Present Age of Grace = 21 years

• Present Age of Sima = 26 years