Question

Q- The present ages of A and B are in the ratio 7:5 , 10 years later their ages will be in ratio 9:7 . Find their present ages.


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Answer 1

Given :

• Ratio of ages of A and B = 7 : 5

• Ratio of ages after 20 years = 9 : 7

To Find :

The present ages of A and B .

Solution :

Let the ages of A and B be 7x and 5x , respectively.

Now , According the question , it said that after 1 years the ratio of ages will be 9 : 5.

So , the age of A after years is (7x + 10) and the age of B after 10 years is (5x + 10) , but we know that the ratio of ages after 10 years is 9 : 5 , so by putting it together , we get the Equation as :

$\underline{\boxed{\bf{\dfrac{7x + 10}{5x + 10} = \dfrac{9}{7}}}}$

By solving the above equation , we can determine the value of x and from there , we can find the present ages of A and B.

By Solving the Equation , we get :

$:\implies \bf{\dfrac{7x + 10}{5x + 10} = \dfrac{9}{7}}$

By multiplying 7 on both the Sides , we get :

$:\implies \bf{\dfrac{7x + 10}{5x + 10} \times 7 = \dfrac{9}{7} \times 7}$

$:\implies \bf{\dfrac{(7x + 10)}{5x + 10} \times 7 = \dfrac{9}{\not{7}} \times \not{7}}$

$:\implies \bf{\dfrac{49x + 70}{5x + 10} = 9}$

By multiplying (5x + 10) on both sides, we get :

$:\implies \bf{\dfrac{49x + 70}{5x + 10} \times (5x + 10) = 9(5x + 10)}$

$:\implies \bf{49x + 70 = 9(5x + 10)}$

$:\implies \bf{49x + 70 = 45x + 90}$

$:\implies \bf{49x - 45x = 90 - 70}$

$:\implies \bf{4x = 20}$

$:\implies \bf{x = \dfrac{20}{4}}$

$:\implies \bf{x = 5}$

Hence, the value of x is 5.

Now , putting the value of x in the present ages of A and B (in terms of x) , we get :

• A's present age = 7x

⠀⠀⠀⠀⠀⠀⠀⠀⠀→ 7 × 5

⠀⠀⠀⠀⠀⠀⠀⠀⠀→ 35 years.

• B's present age = 5x

⠀⠀⠀⠀⠀⠀⠀⠀⠀→ 5 × 5

⠀⠀⠀⠀⠀⠀⠀⠀⠀→ 25 years.

Hence, the present ages of A and B are 35 years and 25 years.

Answer 2

$\underline{\underline{\sf\pink{Given:}}}$

• Ratio of present age of A and B = 7:5
• After 10 years Ratio of their age = 9:7

$\underline{\underline{\sf\pink{Find:}}}$

• Present age of A and B

$\underline{\underline{\sf\pink{Solution:}}}$

Let,

$\sf \begin{gathered}\red{ \sf Present \: age \: of \:A = 7x}\\ \sf \blue{Present \: age \: of \:B = 5x} \end{gathered} \xrightarrow{10 \: years \: later} \begin{gathered} \green{\sf Age \: of \: A = 7x + 10} \\ \orange{\sf Age \: of \:B = 5x + 10} \end{gathered}$

Now, it is given that After 10 years Ratio of their ages will be 9:7

So,

$\mathbb{ACCORDING \: TO \: QUESTION}$

$\sf \to\dfrac{7x + 10}{5x + 10} = \dfrac{9}{7}$

By cross Multiplication

$\sf \to 7(7x + 10) = 9(5x + 10)$

$\sf \to 49x + 70 = 45x + 90$

Collect like terms

$\sf \to 49x - 45x = 90 - 70$

$\sf \to 4x = 20$

$\sf \to x = \dfrac{20}{4} = 5$

$\sf \to x = 5$

$\rule{300}{4}$

Now, we have to find the present values of A and B

So,

Present age of A = 7x = 7×5 = 35years

Present age of B = 5x = 5×5 = 25years

$\rule{300}{4}$