Question

10. The ratio of Reema's age to Sudha's age is 1 : 5. Ten
years later, the ratio of their ages will be 3: 7. Find
their present ages.
​

Answer 1

$\red{\bigstar}$ The present ages are

Reema $\large\leadsto\boxed{\tt\purple{5 \: years}}$

Sudha $\large\leadsto\boxed{\tt\purple{25 \: years}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Given:-

Ratio of Reema's age to Sudha's age = 1:5

Ten years later the ratio will be = 3:7

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• To Find:-

Present ages.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Solution:-

Let the present age of Reema be 'x' and that of Sudha be 'y'.

• According to the question:-

✯ Ratio of Reema's age to Sudha's age is 1:5.

Hence,

➪ $\sf \dfrac{x}{y} = \dfrac{1}{5}$

➪ $\sf x \times 5 = 1 \times y$

➪ $\sf 5x = y$

➪ $\sf y = 5x \dashrightarrow\bf\red{[eqn.i]}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Now,

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

✯ Ratio of Reema's age to Sudha's age after 10 years will be 3:7.

Hence,

➪ $\sf \dfrac{x + 10}{y +10} = \dfrac{3}{7}$

➪ $\sf 7(x+10) = 3(y+10)$

➪ $\sf 7x + 70 = 3y + 30$

➪ $\sf 7x + 70 - 30 = 3y$

➪ $\sf 7x + 40 = 3y$

➪ $\sf 7x - 3y = -40\dashrightarrow\bf\red{[eqn.ii]}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Substituting eqn.[i] in eqn.[ii]:-

➪ $\sf 7x - 3y = -40$

➪ $\sf 7x - 3(5x) = -40$

➪ $\sf 7x - 15x = -40$

➪ $\sf - 8x = - 40$

➪ $\sf x = \dfrac{-40}{-8}$

★ $\large{\underline{\underline{\rm\pink{x = 5}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Substituting the value of x in [eqn.i]:-

➪ $\sf y = 5x$

➪ $\sf y = 5 \times 5$

★ $\large{\underline{\underline{\rm\pink{y = 25}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Therefore, the ages are

Reema = 5 years

Sudha = 25 years

Answer 2

Answer:

THE PRESENT AGE OF REEMA= 5 YEARS

THE PRESENT AGE OF SUDHA = 25 YEARS

Step-by-step explanation:

PARAMETERS GIVEN,

RATIO OF REEMA'S AGE TO SUDHA'S AGE = 1:5

LET THE COMMON RATIO BE x

SO,

AGE OF REEMA = x

AGE OF SUDHA = 5x

AFTER 10 YEARS,

AGE OF REEMA = (x+10)

AGE OF SUDHA = (5x+10)

NOW,

THE RATIO OF AGE OF REEMA TO AGE OF SUDHA=3:7

SO,

A.T.Q.,

(x+10)/(5x+10) = 3/7

7(x+10) = 3(5x+10)

7x+70 = 15x+30

70-30 = 15x-7x

40=8x

x=40/8

x=5

SO,

PRESENT AGE OF REEMA=x=5

PRESENT AGE OF SUDHA = 5x=25

I HOPE YOU UNDERSTOOD THE QUESTION!!!