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

Answer:

Let age of two sisters be x and y,

x−y=10 (1)

x−15=20 (2)

x−15=2(y−15) (3)

Substituting (2) in (3)

20=2y−30

50=2y

y=25 (4)

Substituting (4) in (1)

x−25=10

x=35

Their present ages are 35 years and 25 years.

Step-by-step explanation:

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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

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To find:

• The ratio of their ages 15 years hence?

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Solution:

The difference between the ages of two sisters is 10 years.

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⠀⠀⠀⌬ Let age of younger sister be x years.

⠀⠀⠀⌬ Then, Age of elder sister is (x + 10) years.

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Fifteen years ago their ages were in the ratio 2:1.

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☯ Their ages before 15 year,

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• Age of elder sister = ((x + 10) - 15) years
• Age of younger sister = (x - 15) years

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$\underline{\sf{\bigstar\; According\;to\;the\;question\;:}}$

$:\implies\sf \dfrac{(x + 10) - 15}{x - 15} = \dfrac{2}{1}$

$:\implies\sf (x + 10) - 15 = 2(x - 15)$

$:\implies\sf x - 5 = 2x - 30$

$:\implies\sf x - 2x = - 30 + 5$

$:\implies\sf - x = - 25$

$:\implies{\underline{\boxed{\sf{x = 25}}}}\;\bigstar$

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Therefore,

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⠀⠀⠀⌬ Age of younger sister, x = 25 years

⠀⠀⠀⌬ Then, Age of elder sister, (x + 10) = (25 + 10) = 35 years

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Now, Finding ratio of their ages 15 years hence,

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Their ages after 15 years

• Age of elder sister = 35 + 15 = 50 years
• Age of younger sister = 25 + 15 = 40 years

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☯ Ratio of their ages after 15 years,

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$:\implies\sf \cancel{ \dfrac{50}{40}} = \bf{ \dfrac{5}{4}}$