Question

37 Pens and 53 Pencils cost Rs. 955 while 53 Pens and 37 Pencils together cost Rs. 1115. Find the cost of a pen and that of a pencil ​

Answer 1

..

Step-by-step explanation:

ANSWER

Given :

IN Ist CASE

Number of pens = 37

Number of pencils = 53

Together cost = Rs 320

IN IInd CASE

Number of pens = 53

Number of pencils = 37

Together cost = Rs 400

To find : The cost of a pen and that of a pencil.

Let the cost of the pen be Rs " x "and

That of pencil be Rs " y ".

Then, According to given question

37x + 53y = 320 --------- ( i )

and, 53x + 37y = 400 ------ ( ii )

Now we are , Adding the equations (i) and (ii)

Then we get :

90x + 90y = 720 ⇒ x + y = 8 ----- ( iii )

Now subtract eq ( i ) and ( ii ) ,

We get :

16x - 16y = 80 ⇒ x - y = 5 ----------- ( iv )

Add equation ( iii ) and ( iv )

We get :

2x = 13 ⇒ x = 6.5

\implies \boxed{\mathsf{x\:=\:6.5}}⟹

x=6.5

Subtract x = 6.5 in equation ( iii ) ,

We get :

y = ( 8 - 6.5 )

\implies \boxed{\mathsf{y\:=\:1.5}}⟹

y=1.5

ATLAST, I AM GOING TO CONCLUDE THE WHOLE ANSWER

CostOfOnePen=Rs6.50.

And

CostOfOnePencil=Rs1.50.

Answer 2

Answer:

Cost of pen = ₹16.5

Cost of pencil = ₹6.5

Step-by-step explanation:

Let the cost of one pen be ₹x and the cost of one pencil be ₹y.

∴ According to first condition

  37 x  +  53 y = 955  - (1) and

∴ According to second condition

  53 x  +  37 y = 1115   -(2)

 Adding equations (1) and (2)

  37 x + 53 y =   955

 + 53 x + 37 y  = 1115

 90 x + 90 y = 2070 - (3)

Dividing by 90 on both the sides

   x + y = 23

Subtracting equation (1) from (2)

 53 x +  37 y = 1115

- 37 x +  53 y =  955

16 x  - 16 y  =  160

Dividing by 16 on both the sides

   x  -  y  = 10 - (4)

Adding (3) and (4)

x  + y  =  23

+x  - y   =  10

2 x =  33

 x = 16.5

Put in equation (3)

16.5 + y = 23

y = 23 - 16.5

y = 6.5