Question

The present age of David's mother is 1 more than four times his present age. After 15 years, the ratio of David's age to his mother's age is 1:2. Find the present age of david ​

Answer 1

Answer:−‾‾\mathfrak{\large{\underline{\underline{Answer:-}}}}

Answer:−

Present age of David is 7 years.

Explanation:−‾‾\mathfrak{\large{\underline{\underline{Explanation:-}}}}

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 :-

x+154x+16=12\dfrac{x + 15}{4x + 16} = \dfrac{1}{2}

4x+16

x+15

=

2

1

By cross multiplication :-

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

2x+30=4x+162x + 30 = 4x + 162x+30=4x+16

30=4x+16−2x30 = 4x + 16 - 2x30=4x+16−2x

30=2x+1630 = 2x + 1630=2x+16

30−16=2x30 - 16 = 2x30−16=2x

14=2x14 = 2x14=2x

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

2

14

=x

x=7x = 7x=7

Present age of David = x = 7 years

Verification:−‾‾\mathfrak{\large{\underline{\underline{Verification:-}}}}

Verification:−

Let us check

7+154(7)+16=12\dfrac{7 + 15}{4(7) + 16} = \dfrac{1}{2}

4(7)+16

7+15

=

2

1

2228+16=12\dfrac{22}{28 + 16} = \dfrac{1}{2}

28+16

22

=

2

1

2244=12\dfrac{22}{44} = \dfrac{1}{2}

44

22

=

2

1

22÷2244÷22=12\dfrac{22 \div 22}{44 \div 22} = \dfrac{1}{2}

44÷22

22÷22

=

2

1

12=12\dfrac{1}{2} = \dfrac{1}{2}

2

1

=

2

1

Answer 2

Answer:

David's present Age 7 and Mothers 29.

Step-by-step explanation:

Let M be Mothers Present Age and D be David's.

now let's make 2 Equations from given to solve the Puzzle.

M= 4D. + 1................(1)

This comes From :The present age of David's mother is 1 more than four times his present age.

M + 15 = 2( D+15)..... (2)

this Comes from :After 15 years, the ratio of David's age to his mother's age is 1:2. Find the present age of david

Using (1) , we substitute M in (2)

4D+1+15 = 2D+30

or

2D = 14

D=:7

M= 2D+1=29. from (1)

verifying from 2

29 +15 = 44 = 2x(7+15) =:44