Question

QueStion:-

The sum of the ages of a daughter and her mother is 56 years. After four years, the age of the mother will be three times that of the daughter. Find their present ages.
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ThaNks❤️ ;D​

Answer 1

GIVEN :

• The sum of the ages of a daughter and mother is 56 years. After four years, the age of the mother will be three times that of the daughter.

TO FIND :

• The present age of daughter and mother = ?

SOLUTION :

• Let the age of mother be x years, then the age of daughter would be (56 - x) years.

• After four years, the age of the mother will be (x + 4) and that of the daughter would be (56 - x + 4)years.

★ According to question :-

➨ (x + 4) = 3(56 - x + 4)

➨ x + 4 = 168 - 3x + 12

➨ x + 3x = 168 + 12 - 4

➨ 4x = 176

➨ x = 176/4

➨ x = 44

Therefore, the age of mother is 44 years and age of daughter is (56 - x) = 56 - 44 = 12 years.

Answer 2

GivEn:-

• The sum of the ages of a daughter and her mother is 56 years.

• After four years, the age of the mother will be three times that of the daughter.

To find:-

• Present age of daughter and mother.

SoluTion:-

☯ Let's the present age of daughter be x years.

☯ Let's the present age of Mother be y years.

$\dag\;{\underline{\underline{\bf{\pink{According\;to\;QuesTion:-}}}}}$

The sum of the ages of a daughter and her mother is 56 years.

$:\implies\sf \underline{x + y = 56} .....(1)$

$:\implies\sf y = 56 - x .....(2)$

✠ After Four years -

☯ The age of daughter = (x + 4) years

☯ The age of mother = (y + 4) years

As giVen,

✠ After four years, the age of the mother will be

⠀ three times that of the daughter.

$:\implies\sf y + 4 = 3(x + 4)$

$:\implies\sf y + 4 = 3x + 12$

$:\implies\sf y - 3x = 12 - 4$

$:\implies\sf y - 3x = 8 ....(3)$

Now,

★ Subtracting eq(1) form eq(3) -

$:\implies\sf (x + y) - (y - 3x) = 56 - 8$

$:\implies\sf x \cancel{+ y} \cancel{- y} + 3x = 48$

$:\implies\sf x + 3x = 48$

$:\implies\sf 4x = 48$

$:\implies\sf x = \dfrac{48}{4}$

$:\implies{\underline{\underline{\bf{\blue{x = 12}}}}}$

★ Substituting value of x in eq(2) -

$:\implies\sf y = 56 - x$

$:\implies\sf y = 56 - 12$

$:\implies{\underline{\underline{\bf{\blue{y = 44}}}}}$

$\dag$ Hence, The present age of daughter is 12 years and her mother's is 44 years.

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