Question

43. The ages of Varma and Vishnu are in the ratio 5:7. Four years
from now, the ratio of their ages will be 3:4. Find their present ages.​

Answer 1

Given:

• The ages of Varma and Vishnu are in the ratio of 5: 7.
• Four years from now, the ratio of their ages will be 3: 4.

To find:

• The present age of Varma & Vishnu?

Solution: Let's say, the present ages of Varma and Vishnu be 5x and 7x years respectively.

☆ Four years from now, their ages —

• Varma's age = (5x + 4) years
• Vishnu's age = (7x + 4) years

A/Q,

• As per given condition, Four years from now the ratio of their ages (Vishnu's age & Varma's age) will be 3: 4.

Therefore,

$:\implies\sf \bigg\{\dfrac{5x + 4}{7x + 4}\bigg\} = \bigg\{\dfrac{3}{4}\bigg\} \\\\\\:\implies\sf 4 \Big\{5x + 4\Big\} =3 \Big\{7x + 4\Big\} \\\\\\:\implies\sf 20x + 16 = 21x + 12 \\\\\\:\implies\sf 20x - 21x = 12 - 16 \\\\\\:\implies\sf -x = -4 \\\\\\:\implies\underline{\boxed{\frak{\pmb{\purple{x = 4}}}}}\:\bigstar$

Hence,

• Present age of Varma = 5x = 5(4) = 20 years

• Present age of Vishnu = 7x = 7(4) = 28 years

∴ Hence, the present ages of Varma and Vishnu is 20 years and 28 years respectively.

$\rule{150px}{.3ex}$

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V E R I F I C A T I O N :

• It is given that, Four years from now the ratio of their ages (Vishnu's age & Varma's age) will be 3: 4. So, let's verify :

⠀⠀⠀⠀

$\dashrightarrow\sf \dfrac{5x + 4}{7x + 4} = \dfrac{ 3}{4} \\\\\\\dashrightarrow\sf \dfrac{5(4) + 4}{7(4) + 4} = \dfrac{3}{4} \\\\\\\dashrightarrow\sf \dfrac{20 + 4}{28 + 4} = \dfrac{3}{4} \\\\\\\dashrightarrow\sf \cancel\dfrac{24}{32}^{\;\;8} = \dfrac{3}{4} \\\\\\\dashrightarrow\boxed{\underline{\frak{\dfrac{3}{4} = \dfrac{3}{4}}}}$

⠀⠀⠀⠀

$\qquad\quad\therefore{\underline{\sf{\pmb{\purple{Hence, Verified!}}}}}$⠀

Answer 2

Given :-

The ages of Varma and Vishnu are in the ratio 5:7. Four years

from now, the ratio of their ages will be 3:4.

To Find :-

Their present ages

Solution :-

Let

Present age of Varma = 5y

Present age of Vishnu = 7y

After 4 years

$\sf \bigg(\dfrac{5y+4}{7y+4} \bigg) = \dfrac{3}{4}$

4(5y + 4) = 3(7y + 4)

20y + 16 = 21y + 12

21y - 20y = 16 - 12

y = 4

So,

Present age of Varma = 5(4) = 20 years

Present age of Vishnu = 7(4) = 28 years