Question

ages of rohit and Mohawk are in the ratio 5:7 after 20 years age of rohit and mahawk will be7:9. find the present ages

Answer 1

Let the age of Rohit =5x and Mohawk=7x
After 20 years
Rohit=5x+20/7x+20=7/9
45x+180=49x+140
4x=40
x=10
Present age of Mohit = 50 years and Mohawk = 70 years

Answer 2

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

• Present age of Rohit and Mahawk are in ratio of 5 : 7
• After 20 year ratio of age = 7 : 9

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

• Present age of Rohit and Mahawk

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

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

After 20 years,

• $\: \: \: \: \: Age \: \: of \: \: Rohit \: \: = \: \: {5x} \: + \: {20}$
• $\: \: \: \: \: Age \: \: of \: \: Mahawk \: \: = \: \: {7x} \: + \: {20}$

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

$\: \: \: \: \: \: \: {({5x} \: + \: {20})} \: : \: {({7x} \: + \: {20})} \: \: = \: \: {7} \: : \: {9}$

$\: \: \: \: \: \: \: \leadsto \: \: \frac{({5x} \: + \: {20})}{({7x} \: + \: {20})} \: \: = \: \: \frac{7}{9}$

$\: \: \: \: \: \: \: \leadsto \: \: {9} \: {({5x} \: + \: {20})} \: \: = \: \: {7} \: {({7x} \: + \: {20})}$

$\: \: \: \: \: \: \: \leadsto \: \: {45x} \: + \: {180} \: \: = \: \: {49x} \: + \: {140}$

$\: \: \: \: \: \: \: \leadsto \: \: {45x} \: - \: {49x} \: \: = \: \: {140} \: - \: {180}$

$\: \: \: \: \: \: \: \leadsto \: \: {-4x} \: \: = \: \: {-40}$

$\: \: \: \: \: \: \: \leadsto \: \: {x} \: \: = \: \: \frac{-40}{-4}$

$\: \: \: \: \: \: \: \leadsto \: \: {x} \: \: = \: \: {10}$

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

$\: \: \: \: \: \: \: \leadsto \: \: {5} \: \times \: {10}$

$\: \: \: \: \: \: \: \leadsto \: \: {50} \: years.$

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

$\: \: \: \: \: \: \: \leadsto \: \: {7} \: \times \: {10}$

$\: \: \: \: \: \: \: \leadsto \: \: {70} \: years.$

$\: \: \: \: \: \: \: Hence, \\ \ \: \: Present \: \: age \: \: of \: \: Rohit \: \: and \: \: Mahawk is \: \: {50} \: \: years \: \: and \: \: {70} \: \: years.$

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