Question

the ages of Sona and Sonali are in the ratio 5 is to 35 years hence, the ratio of the ages will be 10 is 27 find their present ages​

Answer 1

Correct Question :

The ages of Sona and Sonali are in the ratio 5 : 3. 5 years hence, the ratio of the ages will be 10 : 7. Find their present ages.

AnswEr :

Let the Present Age of Sona be 5x Yrs. and, Present Age of Sonali be 3x Yrs..

• Five Years from Now :

◗ Sona = (Present + 5) = (5x + 5) Years

◗ Sonali = (Present + 5) = (3x + 5) Years

• According to the Question Now :

⇒ Ratio Of Ages after 5 Years = 10 : 7

⇒ Sona : Sonali = 10 : 7

⇒ (5x + 5) : (3x + 5) = 10 : 7

• Product of Mean = Product of Extreme

⇒ (5x + 5) × 7 = 10 × (3x + 5)

⇒ 35x + 35 = 30x + 50

⇒ 35x - 30x = 50 - 35

⇒ 5x = 15

• Dividing Both term by 5

⇒ x = 3

• Present Ages will be :

◗ Sona = 5x = (5 × 3) = 15 Years

◗ Sonali = 3x = (3 × 3) = 9 Years

∴ Therefore, Present Age of Sona is 15 Years and Present Age of Sonali is 9 Years.

━━━━━━━━━━━━━━━━━━━━━━━━

• Shortcut Trick to Solve Question :

⋆ Present Age⠀⠀➞ 5 Yrs.⠀⋆ Future Age

Sona : Sonali⠀⠀⠀⠀⠀⠀⠀⠀⠀Sona : Sonali

⠀⠀5 : 3⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀10 : 7

◗ Difference of both Ratios is

(5 - 3) = 2 and, (10 - 7) = 3, we will Multiply them by Opposite terms. Means by 3 in Present and By 2 in Future to make Difference Equal.

⠀⠀5 : 3⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀10 : 7

× 3 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀× 2

_______________________________

⠀⠀15 : 9⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀20 : 14

Now, Difference Between Ratios are Same, i.e. (15 - 9) = (20 - 14) = 6.

So, we will find the Difference of Ratio in Ages, that Means we can find from like Sona (20 - 15) = 5 or, Sonali (14 - 9) = 5.

Divide Year Gap By that Number.

↦ Year Gap / Difference of Age

↦ 5 Years / 5

↦ 1

Now, Just Multiply the Outcome (1 in this Case) with any of the Ratio of find Age. Here we have to Find Present Age :

◗ Sona = (15 × 1) = 15 Years

◗ Sonali = (9 × 1) = 9 Years

∴ Therefore, Present Age of Sona is 15 Years and Present Age of Sonali is 9 Years.

Answer 2

Answer:

Correct Question:-

The ages of Sona and Sonali are in the ratio of 5:3. 5 years hence, the ratio of the ages of will be 10:7.Find their present ages.

Solution:-

Let the present age of Sona be 5X years.

Let the present age of Sonali be 3X years.

Then 5 years hence,

Sona's age will be (X+5) years.

Sonali's age will be (3X+5) years.

First equation:-

(5X+5):(3X+5)=10:7

$\implies\frac{5X+5}{3X+5}=\frac{10}{7}$

$\implies\ 7(5X+5)=10(3X+5)$

$\implies\ 35X+35=30X+50$

$\implies\ 35X=30X+50-35$

$\implies\ 35X-30X=15$

$\implies\ 5X= 15$

$\implies\ X =\frac{15}{5}$

$\implies\ X =3$

$\implies\ 5X =3 \times 5$

$\implies\ 5X =15$

So, Sona's present age is 15

years.

Putting the value of X,

$\implies \: So, 3X =3 \times 3$

$\implies\: So, 3X =9$

So, Sonali's present age is 9

years.

Therefore,present age of Sona is 15 years and present age of Sonali is 9 years.

Hope it helps you ❤❤❤

Keep following ❤❤❤