Question

The ages of Arun and Rahul are in the ratio 7 : 5. Ten years hence, the ratio of their ages will be 9 : 7. Find their present ages.

The first one to answer will be the brainliest answer​

Answer 1

Step-by-step explanation:

$\blue{\sf{let \: their \: ages \: be \: 7x \: and \: 5x}} \\ \\ \sf \green{\frac{7x + 10}{5x + 10} = \frac{9}{7} } \\ \\ \sf{ \longrightarrow{7(7x + 10) = 9(5x + 10)}} \\ \sf{ \longrightarrow{49x + 70 = 45x + 90}} \\ \sf{ \longrightarrow{49x - 45x = 90 - 70}} \\ \sf{ \longrightarrow{4x = 20}} \\ \sf{ \longrightarrow{x = \frac{20}{4} = 5 }} \\ x = 5$

$\sf{7 \times 5 = 35yrs} \\ \sf{5 \times 5 = 25yrs}$

$\green{ \boxed{\boxed{\bf \orange{ages = 35yrs \: and \: 25yrs}}}}$

Answer 2

Answer:

Given:-

• Present ages of Arun and Rahul are in the ratio 7 : 5.

• Ten years hence, the ratio of their ages will be 9 : 7.

To Find:-

• Present age of Arun and Rahul.

Step By Step Explanation:

Assumption :

• Let the present age of Arun and Rahul be 7x and 5x.

• Ten years hence, their age will be 7x + 10 and 5x + 10.

Equation :

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According to the given information equation will be ⤵

$\red \bigstar \: \: \: \: \: \: \: \underline{ \boxed{ \bold{ \purple{ \cfrac{7x + 10}{5x + 10} = \cfrac{9}{7}}}}}$

Solution of Equation :-

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Let us solve the above equation !!

$\longmapsto \sf\cfrac{7x + 10}{5x + 10} = \cfrac{9}{7} \\ \\ \longmapsto \sf 7(7x + 10) = 9(5x + 10) \\ \\ \longmapsto \sf 49x + 70 = 45x + 90 \\ \\ \longmapsto \sf 49x - 45x = 90 - 70 \\ \\ \longmapsto \sf 4x = 20 \\ \\ \longmapsto \sf x = \cfrac{ \cancel{20}}{ \cancel4} \\ \\ \longmapsto{\dag \underline{ \boxed {\bold{ \orange{x = 5}}}}} \: \: \: \: \: \dag$

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Therefore, the present

• age of Arun = 7x × 5 = 35 years
• and Rahul = 5x × 5 = 25 years.

Therefore, the present age of Arun is 35 years and Rahul is 25 years.

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