Question

the ratio of the present ages of a mother and daughter is 7:3 . When the mother was 26 years old, the daughter was 6 years old. Find the present age of the mother (in years)

Answer 1

$\Large{\underline{\underline{\mathfrak{\bf{Question}}}}}$

The ratio of the present ages of a mother and daughter is 7:3 . When the mother was 26 years old, the daughter was 6 years old. Find the present age of the mother (in years)

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

$\Large{\underline{\mathfrak{\bf{\pink{Given}}}}}$

• The ratio of the present ages of a mother and daughter is 7:3
• When the mother was 26 years old, the daughter was 6 years old.

$\Large{\underline{\mathfrak{\bf{\pink{Find}}}}}$

• the present age of the mother (in years)

$\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}$

Let,

• Age of mother = x years
• Age of his daughter = y years

A/C to question ,

( The ratio of the present ages of a mother and daughter is 7:3 )

➥ x : y = 7 : 3

➥ x/y = 7/3

➥ 3x - 7y = 0 ..........(1)

Again, A/C to question,

( When the mother was 26 years old, the daughter was 6 years old. )

➥ (x - 26) = (y -6)

➥ x - y = 20 ...............(2)

Multiply by 3 in equ(2), and subtract by (1) - (2),

• 3x - 7y = 0
• 3x - 3y = 60

____________sub. its(Eliminate x )

➥ - 4y = - 60

➥ y = (-60)/(-4)

➥ y = 15

Keep value of y in equ(2)

➥ (x - 15) = 20

➥ x = 20 + 15

➥ x = 35

Thus:-

• Age of mother = 35 years
• Age of his daughter = 15 years

$\Large{\underline{\mathfrak{\bf{\pink{Answer\:Verification}}}}}$

First Condition :-

( The ratio of the present ages of a mother and daughter is 7:3 )

➥ x/y = 7/3

➥ 35/15 = 7/3

( Divide by 5 )

➥ 7/3 = 7/3

➥ 7:3 = 7:3

L.H.S. = R.H.S.

Second condition :-

( When the mother was 26 years old, the daughter was 6 years old.)

➥ (x -26 ) = (y -6)

➥ ( 35 - 26) = ( 15 -6)

➥ 9 = 9

L.H.S. = R.H.S.

That's proved

Answer 2

Step-by-step explanation:

\Large{\underline{\underline{\mathfrak{\bf{Question}}}}}

Question

The ratio of the present ages of a mother and daughter is 7:3 . When the mother was 26 years old, the daughter was 6 years old. Find the present age of the mother (in years)

\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}

Solution

\Large{\underline{\mathfrak{\bf{\pink{Given}}}}}

Given

The ratio of the present ages of a mother and daughter is 7:3

When the mother was 26 years old, the daughter was 6 years old.

\Large{\underline{\mathfrak{\bf{\pink{Find}}}}}

Find

the present age of the mother (in years)

\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}

Explanation

Let,

Age of mother = x years

Age of his daughter = y years

A/C to question ,

( The ratio of the present ages of a mother and daughter is 7:3 )

➥ x : y = 7 : 3

➥ x/y = 7/3

➥ 3x - 7y = 0 ..........(1)

Again, A/C to question,

( When the mother was 26 years old, the daughter was 6 years old. )

➥ (x - 26) = (y -6)

➥ x - y = 20 ...............(2)

Multiply by 3 in equ(2), and subtract by (1) - (2),

3x - 7y = 0

3x - 3y = 60

____________sub. its(Eliminate x )

➥ - 4y = - 60

➥ y = (-60)/(-4)

➥ y = 15

Keep value of y in equ(2)

➥ (x - 15) = 20

➥ x = 20 + 15

➥ x = 35

Thus:-

Age of mother = 35 years

Age of his daughter = 15 years

\Large{\underline{\mathfrak{\bf{\pink{Answer\:Verification}}}}}

AnswerVerification

First Condition :-

( The ratio of the present ages of a mother and daughter is 7:3 )

➥ x/y = 7/3

➥ 35/15 = 7/3

( Divide by 5 )

➥ 7/3 = 7/3

➥ 7:3 = 7:3

L.H.S. = R.H.S.

Second condition :-

( When the mother was 26 years old, the daughter was 6 years old.)

➥ (x -26 ) = (y -6)

➥ ( 35 - 26) = ( 15 -6)

➥ 9 = 9

L.H.S. = R.H.S.

That's proved