Question

the present age of David mother is one more than 4 times his present age after 15 years the ratio of David age of this mother's age is 1 ratio 2 find the present age of David​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer:-}}}}$

Present age of David is 7 years.

$\mathfrak{\large{\underline{\underline{Explanation:-}}}}$

Given :- David's mother is 1 more than 4 times his present age. After 15 years their age will be in the ratio 1 : 2

To find :- Present age of David

Solution :-

Let the present age of David be 'x'

David's mother's present age = 1 more than 4 times his present age = 1 more than 4 times 'x' = 4(x) + 1 = 4x + 1

After 15 years

David's age = x + 15

David's mother's age = (4x + 1) + 15 = 4x + 1 + 15 = 4x + 16

Given that their age Ratio after 15 years = 1 : 2

i.e Ratio of age of David and David's mother's age after 15 years = 1 : 2

From the above information we can form an equation

Equation formed :-

$\dfrac{x + 15}{4x + 16} = \dfrac{1}{2}$

By cross multiplication :-

$(x + 15)2 = 1(4x + 16)$

$2x + 30 = 4x + 16$

$30 = 4x + 16 - 2x$

$30 = 2x + 16$

$30 - 16 = 2x$

$14 = 2x$

$\dfrac{14}{2} =x$

$x = 7$

Present age of David = x = 7 years

$\mathfrak{\large{\underline{\underline{Verification:-}}}}$

Let us check

$\dfrac{7 + 15}{4(7) + 16} = \dfrac{1}{2}$

$\dfrac{22}{28 + 16} = \dfrac{1}{2}$

$\dfrac{22}{44} = \dfrac{1}{2}$

$\dfrac{22 \div 22}{44 \div 22} = \dfrac{1}{2}$

$\dfrac{1}{2} = \dfrac{1}{2}$

Answer 2

Hey there

refer to attachment