Question

cost of 3 pencils and 5 erasers is Rs. 34 and cost of 2 pencils and 7 erasers is 30 then cost of a pencil is
A) 8, B) 5, C) 4, D) 2

Answer 1

Answer:

pencil =x

eraser =y

3x+5y=34 1

2x+7y=30 2

now we get multiply the equation 1 is 2

and we get the multiply equation 2 is 3

we have

6x+10y=68 3

and

6x+21y=90 4

substract the equation 4 in equation 3

therefore, the cost of pencil is 8

we have

11y=22

y=2

now put the value of y in equation 3

we have

6x=48

then value of x is 8

Answer 2

Question :-

Cost of 3 pencils and 5 erasers is Rs. 34 and cost of 2 pencils and 7 erasers is 30 then cost of a pencil is

A) 8

B) 5

C) 4

D) 2

$\huge{ \underline{ \underline{ \green{ \sf{ SoLuTiOn :- }}}}}$

Let the cost of pencil is x

and cost of eraser is y .

According to question

Case (1)

• Cost of 3 pencil and 5 erasers = Rs.34

So ,

✍ 3x + 5y = 34 -------------(1)

Case (2)

• Cost of 2 pencil and 7 erasers = Rs.30

So,

✍ 2x + 7y = 30 -------------(2)

Multiply by 2 in equ. (1) and 3 in equ. (2)

✍ 6x + 10y = 68 ------------(3)

✍ 6x + 21y = 90 ------------(4)

Subtracting equ. (3) and (4) =>

=> 6x + 10y - (6x + 21y) = 68 - 90

=> 6x + 10y - 6x - 21y = - 22

=> - 11y = - 22

=> 11y = 22

=> y = 2

Putting y = 2 in equ .(1) =>

3x + 5y = 34

=> 3x + 5×2 = 34

=> 3x + 10 = 34

=> 3x = 34 - 10

=> 3x = 24

=> x = 8

Here ,

${\purple{\boxed{\large{\bold{x \:= 8 \: and \: y =2 }}}}}$

Therefore ,

${\</u><u>r</u><u>e</u><u>d</u><u>{\boxed{\large{\bold{</u><u>T</u><u>he</u><u> </u><u>\</u><u>:</u><u>cost</u><u> </u><u>\</u><u>:</u><u>of\</u><u>:</u><u> </u><u>pencil</u><u> </u><u>\</u><u>:</u><u>=</u><u> </u><u>Rs</u><u>.</u><u> </u><u>8</u><u>}}}}}$

Option A is correct .