Question

8 year ago, Neelam was four times as old as her daughter.8 year hence, Neelam will be two times as old as a daughter find their present ages ​

Answer 1

• Let the present age of Neelam be x.

• Let the present age of her daughter be y.

By data,

8 years ago, Neelam was four times as old as her daughter.

• The age of Neelam before 8 years is x-8

• The age of the daughter before 8 years is y-8

$x - 8 = 4(y - 8) \\ \\ x - 8 = 4y - 32 \\ \\ 32 - 8 = 4y - x \\ \\ 4y - x = 24$

Let the above equation be equation 1.

Again by data,

8 year hence, Neelam will be two times as old as a daughter.

• Neelam's age after 8 years be x+8

• He age of daughter after 8 years is y+8

$x + 8 = 2(y + 8) \\ \\ x + 8 = 2y + 16 \\ \\ x - 2y = 16 - 8 \\ \\ x - 2y = 8$

Let the above equation be equation 2.

Adding equations 1 and 2.

$(4y - x ) + (x - 2y )= 24 + 8 \\ \\ 4y - x + x - 2y = 32 \\ \\ 2y = 32 \\ \\ y = \frac{32}{2} \\ \\ y = 16$

The present age of Neelam's daughter is 16.

Substitute y = 16 in equation 2

$x - 2y = 8 \\ \\ x - 2(16) = 8 \\ \\ x - 32 = 8 \\ \\ x = 8 + 32 \\ \\ x = 40$

The present age of Neelam is 40.

Answer 2

$\large \sf\underline{ \underline{ \red{give n: }}}$

• 8 years ago , Neelam was 4times as old as her daughter.

• 8years hence , Neelam will be two times as old as her faughter.

$\\ \\ \large \sf\underline{ \underline{ \red{to \: find : }}}$

• Present age of Neelam and daughter.

$\\ \\ \large \sf\underline{ \underline{ \red{solution : }}}$

Let the present age of Neelam be 'x' and daughter be 'y'.

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According to question ,

• 8years ago , Neelam was 4times as old as her daughter.

8years ago ,

• Neelam age = (x-8)yrs

• Daughter age = (y-8)yrs

So,

➥ x - 8 = 4(y-8)

➥ x - 8 = 4y - 32

➥ x - 4y = -32+8

➣ x - 4y = -24 ______(1)

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Also ,

• 8years hence , Neelam will be 2times as old as her daughter.

8yrs hence ,

• Neelam age = (x+8)yrs

• Daughter age = (y+8)yrs

So,

➥ x+8 = 2(y+8)

➥ x+8 = 2y+16

➥ x - 2y = 16 - 8

➥ x - 2y = 8

Multiplying both sides by 2, we get..

➥ 2(x - 2y) = 8×2

➣ 2x - 4y = 16 ______(2)

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Substracting equation (2) by equation (1),

➾ (x - 4y) - (2x - 4y) = -24-16

➾ x - 4y - 2x + 4y = -40

➾ -x = -40

∴ x = 40years

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➙ Putting x = 40 in equation (1) , we get...

➛ x - 4y = - 24

➛ 40 - 4y = - 24

➛ - 4y = - 24 - 40

➛ - 4y = - 64

∴ y = 16years

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Hence , age of Neelam is 40yrs and her daughter is 16yrs.