Question

the age of ram and sham is int he ratio 5:7 . Four years from now, the ratio of their age will be 3:4 . Find their present age​

Answer 1

Answer:

Present age of Ram is 20 years

Present age of Sham is 28 years

Step-by-step explanation:

Let,

Present age of Ram = 5x

Present age of Sham = 7x

★ Four years from now,

The age of Ram = 5x + 4

The age of Sham = 7x + 4

Also,

The ratio of their age will be 3 : 4

So,

⇒ $\tt{\dfrac{5x \: + \: 4}{7x \: + \: 4} \: = \: \dfrac{3}{4}}$

⇒ 4 (5x + 4) = 3 (7x + 4)

⇒ 20x + 16 = 21x + 12

⇒ 20x - 21x = 12 - 16

⇒ - 1x = - 4

⇒ x = 4

___________________________

★ Value of 5x :

⇒ 5 (4)

⇒ 20

____________________________

★ Value of 7x :

⇒ 7 (4)

⇒ 28

Therefore,

Present age of Ram is 20 years

Present age of Sham is 28 years

Answer 2

$\huge\star\:\:{\orange{\underline{\blue{\mathcal{Question}}}}}$

The age of ram and sham is in the ratio 5:7 . Four years from now, the ratio of their age will be 3:4 . Find their present age .

$\huge\star\:\:{\orange{\underline{\pink{\mathcal{Answer}}}}}$

Present ages of Sham and Ram are 20 and 28 respectively .

$\:\sf\underline\green{Given}\:$

The of Ram and Sham is in ratio 5 : 7

$\:\sf\underline\red{To\:Find}\:$

Their present ages

$\:\sf\underline\purple{Solution}\:$

Let the present age of Sham be 5x

And Ram's present age be 7x

So According to the statement .

After four years their ages would be ,

Age of Sham = 5x + 4

Age of Ram = 7x + 4

Note : As mentioned in the question the ratio of their ages is 3 ratio 4 .

Hence ,

$\hookrightarrow\:\dfrac{5x\:+\:4}{7x\:+\:4}\:=\:\dfrac{3}{4}$

$\hookrightarrow\:4\:\times\:(5x\:+\:4)\:=\:3\:\times\:(7x\:+\:4)$

$\hookrightarrow\:20x\:+\:16\:=\:21x\:+\:12$

$\hookrightarrow\:20x\:-\:21x\:=\:12\:-\:16$

$\hookrightarrow\:-x\:=\:4$

$\hookrightarrow\:x\:=\:4$

Now , substituting the value of x . We get ,

Sham's age = 5x

• $5\:\times\:4\:=\:20\:years$

Ram's age = 7x

• $7\:\times\:4\:=\:28\: years$

$\huge{\orange{\underline{\red{\mathscr{Important\: Concepts}}}}}$

What is a linear equation ?

Answer : A linear equation is a mathematical statement that has both sides equal that is LHS is equal to RHS and gives a straight line when plotted in a graph .

_________________________________

What are constants and variables ?

Answer : Constants are numbers that have a fixed value . Variables are the terms whose value is unknown . Their value is not fixed while solving linear equations often will at their value as alphabets . Generally they are x , y and z .

_________________________________

Give some examples of linear equations .

Answer :

1. $\hookrightarrow\:x\:+54\:=\:8$
2. $\hookrightarrow\:3y\:+\:4\:=\:32$
3. $\hookrightarrow\:6x\:+\:y\:=\:89$

_________________________________

Learning some basics :-

• For the equations to work they consist of one or more variables .

• A system of equations consist of two two or more equations in one or more variables .

• Therefore a system of equations can have a number of variables .

• When the number of equations is the same as the number of variables there is likely to be a solution for that . Well not guaranteed in all cases

• When an equation has no solution it is called inconsistent .

• When an equation has a solution it is called consistent .

• When each equation gives new information it is called independent equation whereas generally there are dependent equations .