Question

.Shyam is twice as old as Shreya. Five years ago his age was three times Shreya’s age then. Find their present

ages in years.​

Answer 1

Answer:

Given :-

• Shyam is twice as old as Shreya.
• Five years ago, his age was three times Shreya's age.

To Find :-

• What is their present ages.

Solution :-

Let,

$\mapsto \bf Present\: Age_{(Shyam)} =\: x\: years$

$\mapsto \bf Present\: Age_{(Shreya)} =\: y\: years$

According to the question,

$\bigstar$ Shyam is twice as old as Shreya.

$\implies \sf\bold{\purple{x =\: 2y\: ------\: (Equation\: No\: 1)}}$

Again,

❒ Five Years Ago their ages will be :

$\leadsto \sf Age_{(Shyam)} =\: (x - 5)\: years$

$\leadsto \sf Age_{(Shreya)} =\: (y - 5)\: years$

$\bigstar$ Five years ago, his age was three times Shreya's age.

$\implies \sf x - 5 =\: 3(y - 5)$

$\implies \sf x - 5 =\: 3y - 15$

$\implies \sf x - 3y - 5 + 15 =\: 0$

$\implies \sf\bold{\purple{x - 3y + 10 =\: 0\: ------\: (Equation\: No\: 2)}}$

From the equation no 1 and 2 we get,

$\implies \sf x - (x - 3y + 10) =\: 2y - 0$

$\implies \sf {\cancel{x}} {\cancel{- x}} + 3y - 10 =\: 2y - 0$

$\implies \sf 3y - 10 =\: 2y - 0$

$\implies \sf 3y - 2y =\: - 0 + 10$

$\implies \sf\bold{\red{y =\: 10}}$

Again, by putting y = 10 in the equation no 1 we get,

$\implies \sf x =\: 2y$

$\implies \sf x =\: 2(10)$

$\implies \sf x =\: 2 \times 10$

$\implies \sf\bold{\red{x =\: 20}}$

${\small{\bold{\underline{\therefore\: The\: present\: age\: of\: Shyam\: and\: Shreya\: is\: 20\: years\: and\: 10\: years\: respectively\: .}}}}$

Answer 2

$\large\bf \underline {\underline{\sf{ \bold{Given:}}}}$

$\sf→ { \: Shyam \: is \: twice \: as \: old \: as \: Shreya.}$

$\sf →{\: Five \: years \: ago \: his \: age \: was \: three \: times } \\ \sf{ \: \: \: \: \: \: \: of \: Shyam's \: age.}$

$\large\bf \underline \bold {\underline{\sf{To\:find\::}}}$

$\sf→ { Present \: age \: of \: Shyam}\\ \\ </p><p> \sf→ \: {Present \: age \: of \: Shreya. }$

$\large\bf \underline \bold {\underline{\sf{Solution \: : }}}$

$\sf⇢{Let \: the \: present \: age \: of \: Shyam \: be \: x \: years } \\ \\</p><p> \sf⇢ {Let \: the \: present \: age \: of \: Shreya \: be \: y \: years. }$

$\bf{\underline{\sf{\blue{As\:per\:first\:condition:}}}}$

Ram is twice as old as Shyam

Representing mathematically,

x = 2y -----> 1

$\bf{\underline{\sf{\blue{As\:per\:second\:condition:}}}}$

five yearsago his age was three times of Shyam's age.

Ages 5 years ago :-

Ram's age = x - 5 years

Shyam's age = y - 5 years

Representing the second condition mathematically,

➠ x - 5 = 3 ( y - 5)

➠ x - 5 = 3y - 15

➠ x - 3y = - 15 + 5

➠ x - 3y = - 10 -----> 2

Substitute value of x in equation 2,

➠ 2y - 3y = - 10

➠ - y = - 10

➠ y = 10

Substitute value of y in equation 1,

➠ x = 2y ---> 1

➠ x = 2 ( 10)

➠ x = 20

∴ Present age of Ram = x = 20 years

Present age of Shyam = y = 10 years

$\bf{\underline{\boxed{\sf{\purple{Verification:}}}}}$

For first case :-

Ram is twice as old as Shyam

Present age of Ram = x = 20 years

Present age of Shyam = y = 10 years

↠ x = 2y

↠ 20 = 2 (10)

↠ 20 = 20

LHS = RHS.

For second case :-

Five years ago his age was three times of Shyam's age

Ages 5 years ago :-

Ram's age = x - 5 = 20 - 5 = 15 years

Shyam's age = y - 5 = 10 - 5 = 5 years

↠ x - 5 = 3 ( y - 5)

↠ 15 = 3 ( 5 )

↠ 15 = 15

LHS = RHS.

Hence verified.