Question

At present. Amis age is twice bips age and cam is two years older than ami. Two years ago, the respective ratio between bips age at that time and cams age at time, was 4 : 9. What will be amis age four years hence ?

Answer 1

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______Here's your Answer _______

Let bip's age be x yrs.

=> Ami's age = 2x yrs.

=> Cam's age = 2x + 2 yrs

Now,

2 yrs ago,

Age of Bip = x - 2 yrs.

Ami's age = 2x - 2 yrs.

Cam's age = 2x yrs.

A.T.Q.

x - 2 / 2x = 4 / 9


$\frac{x - 2}{2x} = \frac{4}{9} \\ \\ = > 9x - 18 = 8x \\ \\ = >9 x - 8x = 18 \\ \\ = > x = 18$


So,

Bip's age is 18 yrs.

Ami's age is = 36 yrs.

Cam's age = 38 yrs.

Now,

Age of Ami after 4 years = present age + 4

=> 36 + 4

=> 40 yrs.

So, After 4 years Ami's age will be 40 yrs.
✔✔✔✔

Answer 2

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$\underline{\underline{\huge{\textbf{Solution:}}}}$

Given,

$\textit{Statement - 1:}$
Amis Present age is twice bips Present age
$\implies$ Amis Present Age = 2 × Bips Present Age

$\textit{Statement - 2:}$
Cam is two years older than Ami
$\implies$ Cam's Present Age = Amis Present Age+2

$\textit{Statement - 3:}$
Two years ago, the respective ratio between bips age at that time and cams age at time, was 4 : 9.
$\implies$ (Bip's Age two years Ago):(Cam's Age two years Ago) = 4 : 9

Amis Age 4 years hence = ?

$\underline{\large{\textsf{Step-1:}}}$
Assume Bips Present Age as a Variable.

Let Bips Present Age be x

$\underline{\large{\textsf{Step-2:}}}$
Rewrite Statement -1 in terms of Variable

$\implies$ Amis Present Age = 2x -----(1)

$\underline{\large{\textsf{Step-3:}}}$
Rewrite statement -2 in terms of Variable

$\implies$ Cam's Present Age = 2x+2-----(2)

$\underline{\large{\textsf{Step-4:}}}$
Find Age of Bip's and Cam's, Two years ago

Two years Ago,
Age of Bip = Bip's Present Age-2
$\implies$ Age of Bip = x - 2

Two years Ago,
Age of Cam = Cam's Present Age-2
$\implies$ Age of Cam = (2x+2)-2 = 2x

$\underline{\large{\textsf{Step-5:}}}$
Rewrite statement -3 in terms of Variable

$\implies \dfrac{x-2}{2x} = \dfrac{4}{9}$

$\underline{\large{\textsf{Step-6:}}}$
Cross Multiply

$\implies 9(x-2) = 4(2x)$

$\implies 9x-18 = 8x$

$\implies 9x-8x = 18$

$\implies x = 18$

$\therefore$ Bip's Present Age = 18 years

$\underline{\large{\textsf{Step-7:}}}$
Substitute in (1) and (2)

Amis Present Age = 2(18) = 36 years

Cam's Present Age = 2(18)+2 = 38 years

$\underline{\large{\textsf{Step-8:}}}$
Find Amis Age 4 years hence

$\implies$ Amis Age 4 years hence = (Amis Present Age) + 4

$\implies$ Amis Age 4 years hence = (36) + 4 = 40 years.

$\therefore$
$\textsf{Amis Age 4 years hence = \underline{\textbf{40\: years}}}$

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