Question

The age of a is one third of the age ofb.after 15 years the age of a will be half of the age of

b.find their present ages

Answer 1

Let the present ages be A and B
A= 1/3B
3A- B=0.....(1)
after 15years ages will be
(A+15) (B+15)
A+15=1/2(B+15)
2A+30=B+15
2A-B=25-30
2A-B=-15....(2)
on subtracting (1) from (2)
3A-B=0
2A-B=-15
--------------
A = 15
B = 45
hence; A is 15 years old
B is 45 years old

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\:\:$

$\green{\underline \bold{Given :}}$

$\:\:$

• The age of 'a' is one third of the age of b

$\:\:$

• After 15 years the age of 'a' will be half of the age of 'b'

$\:\:$

$\red{\underline \bold{To \: Find:}}$

$\:\:$

• Their present ages

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

Let the present age of 'a' be x

Let the present age of 'b' be y

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$\purple{\underline \bold{According \: to \: the \ question :}}$

$\:\:$

$\purple\longrightarrow$ $\sf x = \dfrac { 1 } { 3 } y$

$\:\:$

$\sf \longmapsto 3x = y$

$\:\:$

$\sf \longmapsto y - 3x = 0$

$\:\:$

$\sf \longmapsto -3x + y = 0$ ------(1)

$\:\:$

$\underline{\bold{\texttt{After 15 yrs ages will be :}}}$

$\:\:$

• a' age = x + 15

$\:\:$

• b's age = y + 15

$\:\:$

So,

$\:\:$

$\purple\longrightarrow$ $\sf x + 15 = \dfrac { 1 } { 2 }\times (y + 15)$

$\:\:$

$\sf \longmapsto x + 15 = \dfrac { y + 15 } { 2 }$

$\:\:$

$\sf \longmapsto 2x + 30 = y + 15$

$\:\:$

$\sf \longmapsto 2x - y = 15 - 30$

$\:\:$

$\sf \longmapsto 2x - y = - 15$ -------(2)

$\:\:$

$\underline{\bold{\texttt{Adding (1) \& (2)}}}$

$\:\:$

$\sf \longmapsto -3x + 2x + y - y = 0 - 15$

$\:\:$

$\sf \longmapsto -x = -15$

$\:\:$

$\bf \dashrightarrow x = 15$

$\:\:$

$\underline{\bold{\texttt{Putting x = 15 in (2)}}}$

$\:\:$

$\sf \longmapsto 2(15) - y = - 15$

$\:\:$

$\sf \longmapsto 30 - y = - 15$

$\:\:$

$\sf \longmapsto y = 30 + 15$

$\:\:$

$\bf \dashrightarrow y = 45$

$\:\:$

Hence 'a' is 15 yrs old & 'b' is 45 yrs old.

$\rule{200}5$