Question

The ratio of the ages of Seeta and Geeta
is 2:7. After 6 years, the ratio of their ages
will be 1:2. What is the difference in their
present ages?
8 years
9 years
10 years
11 years​

Answer 1

GiveN:-

The ratio of the ages of Seeta and Geeta is 2:7. After 6 years, the ratio of their ages will be 1:2.

To FinD:-

Difference in their present ages.

SolutioN:-

Let the present age of Seeta be 2x and Geeta be 7x.

After 6 years their ages will be,

• Seeta = 2x + 6
• Geeta = 7x + 6
• Their ratio is 1:2

According to the question,

:$\large\implies{\sf{\dfrac{2x+6}{7x+6}=\dfrac{1}{2}}}$

By cross multiplying,

:$\large\implies{\sf{2(2x+6)=7x+6}}$

:$\large\implies{\sf{4x+12=7x+6}}$

:$\large\implies{\sf{12-6=7x-4x}}$

:$\large\implies{\sf{6=3x}}$

:$\large\implies{\sf{\dfrac{6}{3}=x}}$

:$\large\implies{\sf{\dfrac{\cancel{6}}{\cancel{3}}=x}}$

:$\large\implies{\sf{2=x}}$

$\large\therefore\boxed{\bf{x=2.}}$

Their present ages:-

1. Seeta = 2x = 2 × 2 = 4 years
2. Geeta = 7x = 7 × 2 = 14 years

Difference between their present ages:-

:$\large\implies{\sf{Difference=14\:years-4\:years}}$

$\large\therefore\boxed{\bf{Difference=10\:years.}}$

Difference between the present ages of Seeta and Geeta is 10 years.

Answer 2

$\huge \sf \underline \red{↝Answer : }$

$\sf{ \boxed{ \underline{ \underline{ \green{ \tt{10years \: }}}}}}$

$\huge \sf \underline \orange{↝To \: Find : }$

• Different in their present ages.

$\huge \sf \underline \pink{↝Given : }$

• The ratio of the ages of seeta and Geeta is 2:7

• After six years , the ratio of their ages will be 1 :2

$\huge \sf \underline \blue{↝solution : }$

$\sf{Let \: the \: present \: age \: of \: seeta \: be \: x}$

$\sf{Let \: the \: present \: age \: og \: geeta \: be \: x}$

$\: \: \: \: \: \: \: \: \sf \underline{↝After \: 6 \: years : }$

$\: \: \: \: \: \: \: \: \: \ \sf{ \star \: seeta \: age \: will \: be \: 2x + 6}$

$\: \: \: \: \: \: \: \: \: \ \sf{ \star \: geeta \: age \: will \: be \: 7x + 6}$

$\: \: \: \: \: \: \: \: \: \ \sf{ \star \: ratio \: will \: be \: 1 : 2}$

$\sf \underline{so}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \dfrac{2x + 6}{7x + 6} = \dfrac{1}{2}}$

$\: \: \: \: \: \: \: \: \: \: \sf \underline{↝Now \: cross \: multiplication }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ ⇢2(2x + 6) = 7x + 6}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{⇢ 4x + 12 = 7x + 6}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ ⇢12 - 6 = 7x - 4x}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{⇢ 6 = 3x}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ ⇢x = \dfrac{6}{3} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{⇢ x = 2}$

$\sf \underline{↝Now \: their \: present \: ages ,}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \underline \red{⤁seeta \: = 2x = 2 \times 2 = 4 \: years}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \underline \red{⤁geeta \: = 7x = 7 \times 2 = 14\: years}$

______________________________________

The difference in ages of seeta and Geeta is,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \underline{14 - 4 = 10 \: years}}$

$\sf \underline \green{ \therefore \: the \: difference \: between \: present \: age \: of \: seeta \: and \: geeta \: is \: 10 \: years}$

$\sf \underline{ \therefore \: 10years}$