Question

John is four times as old as Martha. Five years ago, the sum of their ages was 50. How old are they now?

Answer 1

GIVEN:

• John is four times as old as Martha.
• Five years ago, the sum of their ages was 50

TO FIND:

• What are their present ages ?

SOLUTION:

Let the present age of John be 'x' years and Martha be 'y' years

CASE:- 1)

❍ John is four times as old as Martha.

According to question:-

➝ x = 4y....❶

CASE:- 2)

❍ Five years ago, the sum of their ages was 50

According to question:-

• John's age = (x –5) years
• Martha's age = (y –5) years

➝ (x –5) + (y –5) = 50

➝ x –5 + y –5 = 50

➝ x + y –10 = 50

➝ x + y = 50 + 10

➝ x + y = 60....❷

Put the value of 'x' from equation 1) in equation 2)

➝ 4y + y = 60

➝ 5y = 60

➝ y = $\sf{\cancel\dfrac{60}{5}}$

❮ y = 12 ❯

Put the value of 'y' in equation 1)

➝ x = 4 $\times$ 12

❮ x = 48 ❯

❝ Hence, John's age is 48 years and Martha's age is 12 years ❞

______________________

Answer 2

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Let the present age of John be x and Martha be y.

It is given that, John is four times as old as Martha.

Then, x=4y........... (1)

Five years ago,

John's age = x-5

And, Martha's age = y-5

Then, sum of their ages =(x-5)+(y-5) = 50

$\implies \: x + y - 10 = 50 \:$

$\implies \: x + y = 60 \: .........(2)$

Now putting the value of equation (1) in equation (2),we get

➡ 4y+y=60

➡ 5y=60

➡ y = 60/5

➡ y= 12

Now putting y=12 in equation (1),we get

$x = 4 \times 12 = 48$

Hence, the present age of John is 48 years and Martha's age is 12 years.