Question

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

Answer 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,

• $\bf{\star \underline {Equation = 9x + 2x = 55}}$

⠀⠀⠀⠀⠀⠀$\underline {\frak{\star\:Now \: By \: Solving\:for\:x\:in \: the \: Formed \: Equation ::}}$

$\qquad:\implies \sf{Equation = 9x + 2x = 55}$

$\qquad:\implies \sf{ 9x + 2x = 55}$

$\qquad:\implies \sf{ 11x = 55}$

$\qquad:\implies \sf{x = \cancel {\dfrac{55}{11}}}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  x = 5\:yrs }}}}\:\bf{\bigstar}$

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,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm { Hence\:Their\:Present \:ages\:area \:\bf{45\:yrs\:\&\:10yrs\: }}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

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

As , We know that ,

• $\bf{\star \underline {Equation = 9x + 2x = 55}}$

Where ,

• $\qquad:\implies \sf{ x = 5}$

⠀⠀⠀⠀⠀⠀$\underline {\frak{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad:\implies \sf{ 9 \times 5 + 2 \times 5 = 55}$

$\qquad:\implies \sf{ 45 + 2 \times 5 = 55}$

$\qquad:\implies \sf{ 45 + 10 = 55}$

$\qquad:\implies \sf{ 55 = 55}$

⠀⠀⠀⠀⠀$\therefore {\underline {\bf{ Hence, \:Verified \:}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

Answer 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,

$\mathfrak{It \: has \: been \: given \: that,}$

• 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.

$\boxed{\sf \implies 9x + 2x = 55}$

Adding 9x and 2x,

$\boxed{\sf \implies 11x = 55}$

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

$\boxed{\sf \implies x = \dfrac{55}{11}}$

Dividing 55 by 11,

$\overline{\boxed{ \sf \implies x = 5.}}$

• The value of x = 5.

----------------------------

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

$\tt 9x = 9 \times 5 = 45.$

$\tt2x = 2 \times 5 = 10.$

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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

$\Rightarrow \sf 9 \times 5 + 2 \times 5$

On simplifying,

$\Rightarrow \sf 45 + 10$

Adding 10 to 45,

$\Rightarrow \sf 55$

RHS

$\Rightarrow \sf 55$

Since LHS = RHS,

Hence verified!