Question

Divide 500/- between rita and seema such that one - third share of rita and half share of seema are equal

with clarity explanation​

Answer 1

$\underline{ \underline{ \Large \pmb{\sf { {Given:}} }} }$

• Total amount = Rs. 500

• One - third share of Rita and half share of Seema are equal.

$\underline{ \underline{ \Large \pmb{\sf { {To \: calculate:}} }} }$

• Divide amount of 500 between Rita and Seema such that one - third share of Rita and half share of Seema are equal.

$\underline{ \underline{ \Large \pmb{\sf { {Calculation:}} }} }$

✰ Here, we are provided that the total amount we have to divide between Rita and Seema is Rs. 500. But the given condition is the we have to divide 500 between the two in such a way that one - third share of Rita and half share of Seema are equal. So, we'll first assume the share of Rita and Seema as variables ( x and y ), then we'll form an algebraic equation and by solving that equation we'll find the value of x and y or share of Rita and Seema.

⠀⠀⠀⠀⠀_____________

Let,

✰ Share of Rita = x

✰ Share of Seema = y

So, as per the given question we have to divide 500 between Rita and Seema. So, the sum of both's share will be equal to 500 i.e,

>> Share of Rita + Share of Seema = 500

$\longrightarrow \sf {x + y = 500 }$

From this equation,

$\longrightarrow \bf { y = 500 - x }$

Let it be equation (i).

⠀⠀⠀⠀⠀⠀⠀⠀⠀________________

✰ According to the question,

$\longrightarrow \sf { \dfrac{1}{3}x = \dfrac{1}{2}y }$

>> Since,we have to divide 500 between the two in such a way that one - third share of Rita and half share of Seema are equal.

Now, substitute the value of y from the equation 1 in order to find the value of x.

$\longrightarrow \sf { \dfrac{1}{3}x = \dfrac{1}{2}(500-x) }$

By using the distributive property we get,

$\longrightarrow \sf { \dfrac{1}{3}x = \dfrac{1}{2}(500) + \dfrac{1}{2}(-x) }$

Perform the multiplication in the right hand side.

$\longrightarrow \sf { \dfrac{1}{3}x = \dfrac{500}{2} - \dfrac{1x}{2} }$

Now, perform the substraction in the right hand side.

$\longrightarrow \sf { \dfrac{1}{3}x = \dfrac{500-1x}{2} }$

By using cross multiplication method, we get :

$\longrightarrow \sf { 2(1x)= 3(500-1x) }$

$\longrightarrow \sf { 2x =1500 - 3x }$

Transposing 3x from RHS to LHS. (While doing transposition, sign changes.)

$\longrightarrow \sf { 2x + 3x =1500 }$

$\longrightarrow \sf { 5x =1500 }$

Transposing 5 from LHS to RHS. (While doing transposition, sign changes.)

$\longrightarrow \sf { x = \cancel{\dfrac{1500}{5}} }$

$\longrightarrow \sf { x = 300 }$

$\longrightarrow \boxed{ \pmb { \rm \red{ Rita's \: share = Rs. \: 300 }}}$

Therefore, Rita's share is Rs. 300.

Also, from the equation (i) :

$\longrightarrow \bf { y = 500 - x }$

$\longrightarrow \sf { y = 500 - 300 }$

$\longrightarrow \sf { y = 200 }$

$\longrightarrow \boxed{ \pmb { \rm \red{ Seema's \: share = Rs. \: 200 }}}$

Therefore, Seema's share is Rs. 200.

Answer 2

Step-by-step explanation:

Let,

✰ Share of Rita = x

✰ Share of Seema = y

So, as per the given question we have to divide 500 between Rita and Seema. So, the sum of both's share will be equal to 500 i.e,

>> Share of Rita + Share of Seema = 500

\longrightarrow \sf {x + y = 500 }⟶x+y=500

From this equation,

\longrightarrow \bf { y = 500 - x }⟶y=500−x

Let it be equation (i).

⠀⠀⠀⠀⠀⠀⠀⠀✰ According to the question,

1/3x= 1/2 x

>> Since,we have to divide 500 between the two in such a way that one - third share of Rita and half share of Seema are equal.

Now, substitute the value of y from the equation 1 in order to find the value of x.

= 1/3 x =1/2(500-x)

By using the distributive property we get,

1/3x =1/2 (500)+1/2 (-x)

Perform the multiplication in the right hand side.

1/3x= 500/2-1x/2

Now, perform the substraction in the right hand side:

1/3= 500-1x/2

By using cross multiplication method, we get :

{ 2(1x)= 3(500-1x) }

⟶2(1x)=3(500−1x)

2x= 1500 -3x

Transposing 3x from RHS to LHS. (While doing transposition, sign changes.)

x= 300

Therefore, Rita's share is Rs. 300.

Also, from the equation (i) :

{ y = 500 - x }⟶y=500−x

{ y = 500 - 300 }⟶y=500−300

{ y = 200 }⟶y=200

Therefore, Seema's share is Rs. 200.

hopefully it will work ☺️☺️