The age of two persons are now the ratio 9:2,The sum of their present ages is 55. Find their present ages.​

2 thoughts on “The age of two persons are now the ratio 9:2,The sum of their present ages is 55. Find their present ages.​”

1. Given : The Present age of two persons are now the ratio 9:2 & sum of their present ages is 55.

   Need To Find : Their Present ages .

   ❍ Let’s Consider their ages be 9x yrs and 2x yrs .

   Given that,

   • The sum of their present ages is 55.

   Therefore,

   • [tex]\bf{\star \underline {Equation = 9x + 2x = 55}}\\[/tex]

   ⠀⠀⠀⠀⠀⠀[tex]\underline {\frak{\star\:Now \: By \: Solving\:for\:x\:in \: the \: Formed \: Equation ::}}\\[/tex]

   [tex] \qquad:\implies \sf{Equation = 9x + 2x = 55}\\[/tex]

   [tex] \qquad:\implies \sf{ 9x + 2x = 55}\\[/tex]

   [tex] \qquad:\implies \sf{ 11x = 55}\\[/tex]

   [tex] \qquad:\implies \sf{x = \cancel {\dfrac{55}{11}}}\\[/tex]

   ⠀⠀⠀⠀⠀[tex]\underline {\boxed{\pink{ \mathrm { x = 5\:yrs }}}}\:\bf{\bigstar}\\[/tex]

   Therefore,

   • The Present age of First Person is 9x = 9 × 5 = 45 yrs .
   • The Present age of Second Person is 2x = 2 × 5 = 10 yrs.

   Therefore,

   ⠀⠀⠀⠀⠀[tex]\therefore {\underline{ \mathrm { Hence\:Their\:Present \:ages\:area \:\bf{45\:yrs\:\&\:10yrs\: }}}}\\[/tex]

   ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

   V E R I F I C A T I O N :

   As , We know that ,

   • [tex]\bf{\star \underline {Equation = 9x + 2x = 55}}\\[/tex]

   Where ,

   • [tex] \qquad:\implies \sf{ x = 5}\\[/tex]

   ⠀⠀⠀⠀⠀⠀[tex]\underline {\frak{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}\\[/tex]

   [tex] \qquad:\implies \sf{ 9 \times 5 + 2 \times 5 = 55}\\[/tex]

   [tex] \qquad:\implies \sf{ 45 + 2 \times 5 = 55}\\[/tex]

   [tex] \qquad:\implies \sf{ 45 + 10 = 55}\\[/tex]

   [tex] \qquad:\implies \sf{ 55 = 55}\\[/tex]

   ⠀⠀⠀⠀⠀[tex]\therefore {\underline {\bf{ Hence, \:Verified \:}}}\\[/tex]

   ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

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2. Answer :–

   • The present ages of the persons are 45 years and 10 years.

   Given :–

   • The age of two persons are in the ratio 9 : 2.

   • The sum of their present ages is 55.

   To find :–

   • Their present ages.

   Step-by-step explanation :–

   • The present ages of two persons are in the ratio 9 : 2.

   • So, let their ages be 9x and 2x.

   Now,

   [tex] \mathfrak{It \: has \: been \: given \: that,} [/tex]

   • The sum of their ages is 55.

   • So, that means the sum of 9x and 2x is equal to 55.

   • Therefore, let’s use this information to form an equation and solve it to find out our answer.

   [tex] \boxed{\sf \implies 9x + 2x = 55}[/tex]

   Adding 9x and 2x,

   [tex] \boxed{\sf \implies 11x = 55}[/tex]

   Transposing 11 from LHS to RHS, changing it’s sign,

   [tex] \boxed{\sf \implies x = \dfrac{55}{11}} [/tex]

   Dividing 55 by 11,

   [tex] \overline{\boxed{ \sf \implies x = 5.}}[/tex]

   • The value of x = 5.

   ––––––––––––––––––––––––––––

   Hence, the present ages of the persons are as follows :–

   [tex] \tt 9x = 9 \times 5 = 45.[/tex]

   [tex] \tt2x = 2 \times 5 = 10.[/tex]

   ———————————————————–

   Verification :–

   To verify our answer, we just have to put 5 (The value of x) in the place of x and see whether LHS = RHS.

   Let’s do it!

   Substituting the value of x in the given equation,

   LHS

   [tex] \Rightarrow \sf 9 \times 5 + 2 \times 5 [/tex]

   On simplifying,

   [tex] \Rightarrow \sf 45 + 10 [/tex]

   Adding 10 to 45,

   [tex] \Rightarrow \sf 55 [/tex]

   RHS

   [tex] \Rightarrow \sf 55 [/tex]

   Since LHS = RHS,

   Hence verified!

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