Question

Ages of joy and Rohit are in the ratio 5:7 . After 10 years, age of Rohit and joy will be 7:9.Find the present ages.​

Answer 1

$\large\underline\pink{Given:-}$

• Present age of Rohit and Joy are in ratio of 5 : 7
• After 10 year ratio of age = 7 : 9

$\large\underline\pink{To find:-}$

• Present age of Rohit and Joy ...?

$\large\underline\pink{Solutions:-}$

• Let the present age of Rohit be 5x years.
• Let the present age of Joy be 7x years.

After 10 years,

• $\: \: \: \: \: Age \: \: of \: \: Rohit \: \: = \: \: {5x} \: + \: {10}$
• $\: \: \: \: \: Age \: \: of \: \: Joy \: \: = \: \: {7x} \: + \: {10}$

$\: \: \: \: \: \underline\red{According \: \: To \: \: Questions:-}$

$\: \: \: \: \: \: \: {({5x} \: + \: {10})} \: : \: {({7x} \: + \: {10})} \: \: = \: \: {7} \: : \: {9}$

$\: \: \: \: \: \: \: \leadsto \: \: \frac{({5x} \: + \: {10})}{({7x} \: + \: {10})} \: \: = \: \: \frac{7}{9}$

$\: \: \: \: \: \: \: \leadsto \: \: {9} \: {({5x} \: + \: {10})} \: \: = \: \: {7} \: {({7x} \: + \: {10})}$

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

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

$\: \: \: \: \: \: \: \leadsto \: \: {-4x} \: \: = \: \: {-20}$

$\: \: \: \: \: \: \: \leadsto \: \: {x} \: \: = \: \: \frac{-20}{-4}$

$\: \: \: \: \: \: \: \leadsto \: \: {x} \: \: = \: \: {5}$

$\: \: \: \: \: \: \: Now,$

$\: \: \: \: \: \: \: \therefore \: \: The \: \: present \: \: age \: \: Rohit \: \: is \: \: {5x}$

$\: \: \: \: \: \: \: \leadsto \: \: {5} \: \times \: {5}$

$\: \: \: \: \: \: \: \leadsto \: \: {25} \: years.$

$\: \: \: \: \: \: \: And$

$\: \: \: \: \: \: \: \therefore \: \: There \: \: present \: \: age \: \: Joy \: \: is \: \: {7x}$

$\: \: \: \: \: \: \: \leadsto \: \: {7} \: \times \: {5}$

$\: \: \: \: \: \: \: \leadsto \: \: {35} \: years.$

$\: \: \: \: \: \: \: Hence, \: \: Present \: \: age \: \: of \: \: Rohit \: \: and \: \: Joy is \: \: {25} \: \: years \: \: and \: \: {35} \: \: years.$

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Answer 2

Answer:

Let the age be x

So, present age of joy is 5x

and present age of Rohit is 7x

After 10 years,

Age of joy = 5x+10

Age of Rohit = 7x+10

According to the question,

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

9(5x+10) = 7(7x+10)

45x+90 = 49x+70

90-70 = 49x-45x

20 = 4x

x = 5

Present age of joy = 5×5 = 25years

Present age of Rohit = 7×5 = 35years