Question

mple-10. Mary told her daughter, "Seven years ago, I was seven times as old as you were
1. Also, three years from now, I shall be three times as old as you will be." Find the present
of Mary and her daughter.​

Answer 1

||✪✪ QUESTION ✪✪||

Mary told her daughter, "Seven years ago, I was seven times as old as you were .. Also, three years from now, I shall be three times as old as you will be." Find the present

of Mary and her daughter. ?

|| ✰✰ ANSWER ✰✰ ||

Lets Assume That, Marry Present age is x years , and her daughter Present age is y years.

Then, Seven years ago,

→ Age of Mary = (x - 7)

→ Age of daughter = (y- 7)

According to the question now,

→ (x - 7) = 7 (y - 7 )

→ x - 7 = 7y - 49

→ x- 7y = - 49 + 7

→ x - 7y = (-42) -------------- Equation (1)

________________________

Now,

Three years from now

→ Age of Mary = x +3

→ Age of daughter = y +3

According to the question :-

→ (x + 3) = 3 (y + 3)

→ x + 3 = 3y + 9

→ x - 3y = 9-3

→ x - 3y = 6 --------------- Equation (2)

________________________

Subtracting Equation (1) From Equation (2) Now, we get,

→ (x - 3y) - (x - 7y) = 6 - (-42)

→ -3y + 7y = 6 + 42

→ 4y = 48

→ y = 12 years.

Putting in Equation (2) now,

→ x - 3*12 = 6

→ x = 6 + 36

→ x = 42 years.

Hence, Mary Present age is 42 years and her daughter Present age is 12 years.

꧁_______________________꧂

Answer 2

Answer:

$\large{\boxed{\star{\mathfrak\green{Present \: age \: of \: Mary = 42 \: years }}}}$

$\large{\boxed{\star{\mathfrak\pink{Present \: age \: of \: daughter= 12 \: years }}}}$

$\rule{200}{1}$

Given:-

• 7 years ago, Mary's age = 7 times her daughter's age.
• 3 years from now, Mary's age = 3 times daughter's age.

To find:-

• Present age of Mary and her daughter

Solution:-

Let present age of Mary and her daughter be x and y years respectively.

${\underline{\bold\red{ATQ:-}}}$

$\rightharpoonup\sf (x - 7) = 7(y - 7) \\\\\rightharpoonup\sf x - 7 = 7y - 49 \\\\\rightharpoonup\sf x = 7y - 49 + 7 \\\\\rightharpoonup\sf x = 7y - 42 - - - - - - - (i)$

2nd case:-

$\rightharpoonup\sf (x + 3) = 3(y + 3) \\\\\rightharpoonup\sf x + 3 = 3y + 9 \\\\\scriptsize\sf \: \: \: [From \: equation \: (i) \: :- ] \\\\\rightharpoonup\sf 7y - 42 + 3 = 3y + 9 \\\\\rightharpoonup\sf 7y - 39 = 3y + 9 \\\\\rightharpoonup\sf 7y - 3y = 9 + 39 \\\\\rightharpoonup\sf 4y = 48 \\\\\rightharpoonup\sf y = 48/4 \\\\\rightharpoonup{\boxed{\sf\green{ y = 12 \: years }}}$

Putting value of y in (i) :-

$\rightharpoonup\sf x = 7(12) - 42 \\\\\rightharpoonup\sf x = 84 - 42 \\\\\rightharpoonup{\boxed{\sf\pink{x = 42 \: years }}}$

$\therefore\bold{Present \: age \: of \: Mary(x) = 42 \: years }$

$\therefore\bold{Present \: age \: of \: daughter(y) = 12 \: years }$