Question

The age of Anjali and Shamli are in the ratio 5:7 . Four years from now, the ratio of their

ages is 3:4. Find their present ages.​​

Answer 1

✫ The present ages of anjali and shamli is 20 and 28 ✫

Step-by-step explanation:

Given:-

• Age of anjali and shamli are in the ratio 5:7.
• Four years from now,the ratio of their ages is 3:4.

To find:-

• Present ages of anjali and shamli.

Solution:-

❍ Let the present ages of anjali and shamli be 5x and 7x respectively.

After 4 years,

• Anjali be = 5x + 4
• Shamli be = 7x + 4

Then,

$\\ :\implies\sf{\frac{5x+4}{7x+4}=\frac{3}{4}}$

cross multiplying the values,we get:

$\\ :\implies\sf{4(5x+4)=3(7x+4)}\\ \\ :\implies\sf{20x+16=21x+12}\\ \\ :\implies\sf{20x-21x=12-16}\\ \\ :\implies\sf{\cancel{-}\;1x=\cancel{-}\;4}\\ \\ :\implies\underbrace{\boxed{\frak{x=4}}}\; \blue{\bigstar}$

Therefore,

• Present age of anjali = 5x
• Present age of anjali = 5(4)
• Present age of anjali = 20

• Present age of shamli = 7x
• Present age of shamli = 7(4)
• Present age of shamli = 28

Hence,

• Present age of anjali and shamli is 20 and 28.

Answer 2

Given:

• The age of Anjali and Shamli are in the ratio 5:7.
• Four years from now, the ratio of their ages is 3:4.

To Find:

• Present age of Anjali and Shamli

Let's Solve:

• So, let their ages be 5x and 7x
• After 4 years their ages will be in ratio 3:4

$\red \bigstar \rm{Anjali \: age = 5x+4 } \\\red \bigstar \rm{Shamli \: age = 7x+4}$

Therefore,

$\implies \rm{4(5x+4)=3(7x+4)} \\ \implies \rm{20x+16=21x+12} \\ \implies \rm{16−12=21x−20x} \\ \implies \rm {4=1x} \\ \fbox \red{ x=4}$

Now,

• Present age of Anjali = 5x

=(5×4)

=20 years

• Present age of Shamli =7x

=(7×4)

=28 years

Hence,

$\green\bigstar$The present age of Anjali = 20 years

$\green\bigstar$The present age of Shmali =28 years

Thank you!

@itzshivani