Question

the difference between the ages of two sisters is 10 years. Fifteen years ago their ages were in the ratio 2:1. find the ratio of their ages 15years hence​

Answer 1

Given :

• Difference between the ages of two sisters is 10 years .
• 15 years ago their ages were in the artio 2:1 .

To Find :

• Ratio of their ages after 15 years .

Solution :

$\longmapsto\tt{Let\:the\:Age\:of\:sister\:A=x}$

$\longmapsto\tt{Age\:of\:sister\:B=x+10}$

Before 15 years :

$\longmapsto\tt{Age\:of\:Sister\:A=x-15}$

$\longmapsto\tt{Age\:of\:Sister\:B=x+10-15=x-5}$

A.T.Q :

$\longmapsto\tt{\dfrac{x-5}{x-15}=\dfrac{2}{1}}$

$\longmapsto\tt{1(x-5)=2(x-15)}$

$\longmapsto\tt{x-5=2x-30}$

$\longmapsto\tt{x-2x=-30+5}$

$\longmapsto\tt{-x=-25}$

$\longmapsto\tt\bf{x=25}$

Value of x is 25 ..

Therefore :

$\longmapsto\tt{Present\:Age\:of\:Sister\:A=x}$

$\longmapsto\tt\bf{25\:yrs}$

$\longmapsto\tt{Present\:Age\:of\:Sister\:B=25+10}$

$\longmapsto\tt\bf{35\:yrs}$

Now ,

After 15 years :

$\longmapsto\tt{Age\:of\:Sister\:A=25+15}$

$\longmapsto\tt\bf{40\:yrs}$

$\longmapsto\tt{Age\:of\:Sister\:B=35+15}$

$\longmapsto\tt\bf{50\:yrs}$

Ratio :

$\longmapsto\tt{\dfrac{5{\not{0}}}{4{\not{0}}}}$

$\longmapsto\tt\bf{\dfrac{5}{4}}$

So , The Ratio is 5:4 ...

Answer 2

Given

• The difference between the ages of two sisters is 10 years.
• Fifteen years ago their ages were in the ratio 2:1.

To find

• Ratio of their ages after 15 years.

Solution

• Let the age of first sister be x
• Then, age of second sister = x + 10

★ 15 years ago

• Age of first sister = x - 15
• Age of second sister = x + 10 - 15 ⠀⠀ ⠀= x - 5

According to the question

→ x - 5/x - 15 = 2/1

→ x - 5 = 2(x - 15)

→ x - 5 = 2x - 30

→ x - 2x = -30 + 5

→ -x = -25

→ x = 25

★ Present age

• Age of first sister = 25 years
• Age of second sister = 25 + 10 = 35 years

★ After 15 years

• Age of first sister will be = 25 + 15

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⟹ 40 years

• Age of second sister will be = 35 + 15

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⟹ 50 years

» Ratio

↬ $\dfrac{50}{40}$

↬ $\dfrac{5\not{0}}{4\not{0}}$

↬ $\dfrac{5}{4}$

↬ $5:4$