Question

Sushil is now 4 times as old as Sunil.Five years ago Sushil was 7 times as old as Sunil was then.Find the present age of each of them.​

Answer 1

AnswEr :

Let the present age of Sunil be x yrs, and present age of Sushil be 4x yrs.

• 5⠀Y E A R S⠀A G O (Past) :

◗ Sunil = Present - 5 = (x - 5) yrs

◗ Sushil = Present - 5 = (4x - 5) yrs

• According to the Question :

↠ Sushil = Seven times of Sunil

↠ 4x - 5 = 7(x - 5)

↠ 4x - 5 = 7x - 35

↠ 4x - 7x = -35 + 5

↠ -3x = -30

↠ 3x = 30

↠ x = 30 ÷ 3

↠ x = 10 yrs

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• P R E S E N T⠀A G E S :

◗ Sunil = x = 10 Years

◗ Sushil = 4x = 4 × 10 = 40 Years

∴ Present Age of Sunil and Sushil will be 10 Years and 40 Years respectively.

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• P O I N T S T O R E M E M B E R :

• If the present age is x, then y times the present age = xy.
• If the present age is x, then age y years later = x + y.
• If the present age is x, then age y years ago = x - y.

Answer 2

AnswEr-:

• $\underline {\dag{\pink{\mathrm{ The \:present \:ages\:of\:Sunil\:and\:Sushil\: are \:10\:years \:and\:40\:years\:respectively}}}}$

Explanation-:

$\mathrm { Given-:}$

• Shushil age is 4 times as old as Sunil .
• Five years ago Sushil was 7 times as old as Sunil.

$\mathrm { To \:Find -:}$

• Present age of Sunil and Sushil.

$\dag{\mathrm { Solution \:of\:Question-:}}$

$\mathrm { Let's\:Assume-:}$

• The present age of Sunil be x yrs .

Then ,

• Shushil age is 4 times as old as Sunil .

• Therefore ,

• Sushil present age be 4x yrs .

Then ,

• $\frak{Their\:present \:age\:\: -:} \begin{cases} \sf{Present \:age\:of\:Sunil\:\:is\:= \frak{x\:yrs}} & \\\\ \sf{ Present \:age\:of\:Sushil\:\:is\:\:=\:\frak{4x\:yrs}}\end{cases}$

$\mathrm { Before \:5 \:years \:their\:ages-:}$

• $\frak{Before \:5 \:years \:their \:age\:\: -:} \begin{cases} \sf{Age\:of\:Sunil\:\:is\:= \frak{x-5\:yrs}} & \\\\ \sf{ Present \:age\:of\:Sushil\:\:is\:\:=\:\frak{4x-5\:yrs}}\end{cases}$

As , Given that ,

• Five years ago Sushil was 7 times as old as Sunil.

Then ,

• $\longrightarrow {\sf{New\:Formed \:Equation \:-:4x -5 = 7(x -5) }}$

Now , Solving for x in Equation-:

• $\longrightarrow {\sf{\:Formed \:Equation \:-:4x -5 = 7(x -5) }}$

• $\longrightarrow {\sf{\:4x -5 = 7(x -5) }}$

• $\longrightarrow {\sf{\:4x -5 = 7x -35 }}$

• $\longrightarrow {\sf{\:4x -7x =- 35 + 5 }}$

• $\longrightarrow {\sf{\:-3x = -30 }}$ [ - sign will be eliminated from both sides ]

• $\longrightarrow {\sf{\:3x = 30 }}$

• $\longrightarrow {\sf{\:x =\: {30}{3} }}$

• $\longrightarrow {\sf{\:x =\:\dfrac {\cancel {30}}{\cancel {3}} }}$

• $\longrightarrow {\sf{\:x =\: 10 yrs }}$

Therefore ,

• $\boxed {\sf{\:x =\: 10 \:yrs }}$

Therefore,

• Putting x = 10 in their ages -:

• $\frak{Putting \:x=5 \:in\:their\:age\:\: -:} \begin{cases} \sf{Present \:age\:of\:Sunil\:\:is\:= \frak{x\:= 10 yrs}} & \\\\ \sf{ Present \:age\:of\:Sushil\:\:is\:\:=\:\frak{4x\:= 4 \times 10 = 40 yrs}}\end{cases}$

Hence ,

• $\underline {\dag{\pink{\mathrm{ The \:present \:ages\:of\:Sunil\:and\:Sushil\: are \:10\:years \:and\:40\:years\:respectively}}}}$

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