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Ratio of present ages of Sona and Sonali is 5:3. After 5 years their ages will be in the ratio 10:7. Calculate the present ages.

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Answer 1

Given :

• Ratio of Present ages of Sona and Sonali = 5:3
• Ratio of their ages after 5 years = 10:7

To Find :

• Present Ages of Sona and Sonali?

Let's Assume:

Let's Assume that the Present ages :

Present Age of Sona = 5x

Present Age of Sonali = 3x

So, their ages after 5 years :

Age of Sona after 5 years = 5x+5

Age of Sonali After 5 years = 3x+5

Concept :

As we don't know their Present ages, so we will Assume their ages (See the let's Assume part) .

Now, with the assumed Quantity, we will compare it with the Ratio to find our the value of variable

hence, we can easily find out their ages

Solution :

As we assumed:

Age of Sona = 5x

Age of Sonali = 3x

Age of Sona after 5 years = 5x+5

Age of Sonali after 5 years = 3x+5

So, now comparing it with the Ratios

$\displaystyle \rm \implies \frac{5x + 5}{3x + 5} = \frac{10}{7}$

$\displaystyle \rm \implies 7(5x + 5) = 10(3x + 5)$

$\displaystyle \rm \implies 35x +35 = 30x + 50$

$\displaystyle \rm \implies 35x - 30x = 50 - 35$

$\displaystyle \rm \implies 5x = 15$

$\displaystyle \rm \implies x = \frac{15}{5}$

$\displaystyle \rm \implies x = 3$

So, we got the value of variable (x) as 3

So, Age of Sona = 5×3 = 15 years.

Age of Sonali = 3×3 = 9

Final Answer:

As we got , the ages are :

• Age of Sona = 15 years
• Age of Sonali = 9 years

Answer 2

Step-by-step explanation:

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