Question

Ten years ago, the age of mother was three times the age of her son. After ten years, mother’s age will be twice that of his son. Find the ratio of their present ages *

Answer 1

Step-by-step explanation:

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Answer 2

$\bf{\huge{\underline{\boxed{\sf{\red{Answer:}}}}}}$

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

• Ten years ago, the age of mother was three times the age of her son.
• After ten years, mother’s age will be twice that of his son

$\bf{\underline{\underline{\sf{\pink{To\:find:}}}}}$

• The ratio of their present ages.

$\bf{\underline{\underline{\sf{\blue{Solution:}}}}}$

Let the present age of Mother be x years.

Let the present age of Son be y years.

$\bf{\underline{\underline{\sf{\blue{As\:per\:first\:condition:}}}}}$

• Ten years ago, the age of mother was three times the age of her son.

Ages 10 years ago :-

• Mother = x - 10 years
• Son = y - 10 years

Representing the condition mathematically.

=> x - 10 = 3 ( y - 10)

=> x - 10 = 3y - 30

=> x - 3y = - 30 + 10

=> x - 3y = - 20 ----> 1

$\bf{\underline{\underline{\sf{\blue{As\:per\:second\:condition:}}}}}$

• After ten years, mother’s age will be twice that of his son

Ages after 10 years :-

• Mother = x + 10 years
• Son = y + 10 years

Representing the condition mathematically.

=> x + 10 = 2 ( y + 10)

=> x + 10 = 2y + 20

=> x - 2y = 20 - 10

=> x - 2y = 10 ----> 2

Solve equations 1 and 2 simultaneously by elimination method.

Subtract equation 2 from equation 1,

...+ x - 3y = - 20

- (+ x - 2y = 10)

--------------------------

- y = - 30

y = 30

Substitute y = 30 in equation 1,

=> x - 3y = - 20

=> x - 3 ( 30) = - 20

=> x - 90 = - 20

=> x = - 20 + 90

=> x = 70

$\bf{\large{\underline{\boxed{\sf{\green{Present\:age\:of\:Mother\:=\:x\:=\:70\:years}}}}}}$

$\bf{\large{\underline{\boxed{\sf{\green{Present\:age\:of\:Son\:=\:y\:=\:30\:years}}}}}}$

To find the ratio of the present age of Mother and Son,

=> Ratio = $\large\frac{x}{y}$

=> Ratio = $\large\frac{70}{30}$

=> Ratio = $\large\frac{35}{15}$

=> Ratio = $\large\frac{7}{3}$

•°• Ratio of the present ages of mother and son = 7 : 3