Question

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

Answer 1

AnswEr :

⠀⠀⠀⠀⠀⠀☯ Given Ratio is 5:3. Let's consider that sona's age be '5x' & Sonali age be '3x'. Five years later ratio of their ages will be 10:7.

$:\implies\tt \dfrac{5x + 5}{3x + 5} = \dfrac{10}{7} \\\\\\:\implies\tt 7 \Big(5x + 5 \Big) = 10 \Big( 3x + 5 \Big) \\\\\\:\implies\tt 35x + 35 = 30x + 50 \\\\\\:\implies\tt 35x - 30x = 50 - 35 \\\\\\:\implies\tt 5x = 15 \\\\\\:\implies\tt x = \dfrac{15}{5} \\\\\\:\implies\underline{\boxed{\tt{\red{ x = 3}}}}$

$\rule{150}2$

$\star\: \sf {\underline{\blue{Now,~ Finding~ age -}}}$

Sona's age - 5x

$:\implies\tt 5 \Big(3 \Big) \\\\\\\maltese\;{\underline{\boxed{\sf{x = 15 \: years}}}}}$

Sonali's age 3x

$:\implies\tt 3 \Big(3 \Big) \\\\\\\maltese\;{\underline{\boxed{\sf{ x = 9~ years}}}}}$

$\rule{150}2$

$\dag\;\sf \underline{Hence, Present \: ages \: of \: sona \:\&\: sonali \: is \: 15 \: \&\: 9 \: years.}$

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Answer 2

Answer:

Present age of Sona is 15 years and Sonali is 9 years.

Step-by-step explanation:

The ages of Sona and Sonali are in the ratio 5:3.

Assume that the age of Sona is 5x years and Sonali is 3x years.

Five years hence:

• Age of Sona = (5x + 5) years
• Age of Sonali = (3x + 5) years

Five years hence, the ratio of their of their ages will be 10:7.

As per given condition,

→ (5x + 5)/(3x + 5) = 10/7

→ 7(5x + 5) = 10(3x + 5)

→ 35x + 35 = 30x + 50

→ 35x - 30x = 50 - 35

→ 5x = 15

→ x = 3

Hence, the age of

• Sona = 5x = 5(3) = 15 years
• Sonali = 3x = 3(3) = 9 years