Question

The ages of Arun and Rahul are in the ratio 7 : 5 Ten years Hance, the ratio of their ages will be 9 : 7. find the present age of Arun and Rahul respectively.​

Answer 1

Answer:

5

Step-by-step explanation:

7x + 10 + 5x + 10 = 9x + 7x

=> 12x + 20 = 16x

=> 16x - 12x = 20

=> 4x = 20

=> x = 20/4

=> x = 5

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Answer 2

Answer

• Present age of Arun = 35 years.
• Present age of Rahul = 25 years.

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 :

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 :

Let us solve the above equation !!

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

Therefore, the present age of Arun = 7x → 35 years and Rahul = 5x → 25 years.

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