Question

the present age of ram and shyam are 4:3 four years later their age is 6:5 find present age​

Answer 1

$\huge\bold{\mathbb{QUESTION}}$

The present age of Ram and Shyam are $4:3.$ Four years later their age is $6:5.$ Find their present ages.

$\huge\bold{\mathbb{GIVEN}}$

• The present age of Ram and Shyam are $4:3.$

• Four years later their age is $6:5.$

$\huge\bold{\mathbb{TO\:FIND}}$

Their present ages.

$\huge\bold{\mathbb{CONCEPT}}$

Linear Equations.

$\huge\bold{\mathbb{SOLUTION}}$

Since the present age of Ram and Shyam are $4:3,$

Let

• Ram's present age be $4x\:yrs.$

• Shyam's present age be $3x\:yrs.$

After $4\:yrs,$

• Ram's age will be $(4x+4)\:yrs.$

• Shyam's age will be $(3x+4)\:yrs.$

But, it is given that $4\:yrs$ years later their ages will be in the ratio $6:5.$

According to condition,

$(4x+4):(3x+4)=6:5$

$\implies {\dfrac{(4x+4)}{(3x+4)}}={\dfrac{6}{5}}$

By cross multiplication.

$\implies 5(4x+4)=6(3x+4)$

Removing parentheses.

$\implies 20x+20=18x+24$

Combining the like terms.

$\implies 20x-18x=24-20$

$\implies 2x=4$

$\implies x={\dfrac{4}{2}}$

$\implies x=\cancel{\dfrac{4}{2}}$

$\implies x=2$

$\huge\bold{\mathbb{HENCE}}$

$x=2$

Present ages of:

Ram $=4x\:yrs=(4\times2)\:yrs=8\:yrs$

Shyam $=3x\:yrs=(3\times2)\:yrs=6\:yrs$

$\huge\bold{\mathbb{THEREFORE}}$

The present ages of Ram and Shyam are $8\:yrs$ and $6\:yrs$ respectively.

$\huge\bold{\mathbb{NOT\:SURE\:??}}$

$\huge\bold{\mathbb{VERIFICATION}}$

$(4x+4):(3x+4)=6:5$

$\implies {\dfrac{(4x+4)}{(3x+4)}}={\dfrac{6}{5}}$

Putting $x=2.$

$\implies {\dfrac{\{(4\times2)+4\}}{\{(3\times2)+4\}}}={\dfrac{6}{5}}$

$\implies {\dfrac{(8+4)}{(6+4)}}={\dfrac{6}{5}}$

$\implies {\dfrac{12}{10}}={\dfrac{6}{5}}$

$\implies {\dfrac{\cancel{12}}{\cancel{10}}}={\dfrac{6}{5}}$

$\implies {\dfrac{6}{5}}={\dfrac{6}{5}}$

So, $L.H.S=R.H.S.$

Hence, verified ✓ .

$\huge\bold{\mathbb{WE\:MADE\:IT\:!!}}$

Answer 2

$\huge\bold{\mathbb{QUESTION}}$

The present age of Ram and Shyam are $4:3.$ Four years later their age is $6:5.$ Find their present ages.

$\huge\bold{\mathbb{GIVEN}}$

The present age of Ram and Shyam are $4:3.$

Four years later their age is $6:5.$

$\huge\bold{\mathbb{TO\:FIND}}$

Their present ages.

$\huge\bold{\mathbb{CONCEPT}}$

Linear Equations.

$\huge\bold{\mathbb{SOLUTION}}$

Since the present age of Ram and Shyam are $4:3,$

Let

Ram's present age be $4x\:yrs.$

Shyam's present age be $3x\:yrs.$

After $4\:yrs,$

Ram's age will be $(4x+4)\:yrs.$

Shyam's age will be $(3x+4)\:yrs.$

But, it is given that $4\:yrs$ years later their ages will be in the ratio $6:5.$

According to condition,

$(4x+4):(3x+4)=6:5$

$\implies {\dfrac{(4x+4)}{(3x+4)}}={\dfrac{6}{5}}$

By cross multiplication.

$\implies 5(4x+4)=6(3x+4)$

Removing parentheses.

$\implies 20x+20=18x+24$

Combining the like terms.

$\implies 20x-18x=24-20$

$\implies 2x=4$

$\implies x={\dfrac{4}{2}}$

$\implies x=\cancel{\dfrac{4}{2}}$

$\implies x=2$

$\huge\bold{\mathbb{HENCE}}$

$x=2$

Present ages of:

Ram $=4x\:yrs=(4\times2)\:yrs=8\:yrs$

Shyam $=3x\:yrs=(3\times2)\:yrs=6\:yrs$

$\huge\bold{\mathbb{THEREFORE}}$

The present ages of Ram and Shyam are $8\:yrs$ and $6\:yrs$ respectively.

$\huge\bold{\mathbb{NOT\:SURE\:??}}$

$\huge\bold{\mathbb{VERIFICATION}}$

$(4x+4):(3x+4)=6:5$

$\implies {\dfrac{(4x+4)}{(3x+4)}}={\dfrac{6}{5}}$

Putting $x=2.$

$\implies {\dfrac{\{(4\times2)+4\}}{\{(3\times2)+4\}}}={\dfrac{6}{5}}$

$\implies {\dfrac{(8+4)}{(6+4)}}={\dfrac{6}{5}}$

$\implies {\dfrac{12}{10}}={\dfrac{6}{5}}$

$\implies {\dfrac{\cancel{12}}{\cancel{10}}}={\dfrac{6}{5}}$

$\implies {\dfrac{6}{5}}={\dfrac{6}{5}}$

So, $L.H.S=R.H.S.$

Hence, verified ✓ .

$\huge\bold{\mathbb{WE\:MADE\:IT\:!!}}$