Question

The cost of 2 pencils and 5 pens is Rs 17, two pencils and 3 pens of the same rate is Rs 11. Find out the prices of a pencil and a pen. *

Answer 1

the cost of 2 pencils and 5 pens=Rs.17

the cost of 2 pencils and 3 pens =Rs.11

the cost of 2 pen=Rs.17-11

=Rs.6

the cost of 1 pen=Rs.6/2

=Rs.3

the cost of 2 pencils =Rs.17-(5*3)

=Rs.17-15

=Rs.2

the cost of 1 pencil=Rs.2/2

=Rs.1

Hence,the cost of 1 pencil is Rs.1 and the cost of 1 pen is Rs.3.

Answer 2

Answer:

${\large{\sf{\underline{Given}}}}$

• Cost of 2 Pencils & 5 pens = ₹17
• Cost of 2 pencils & 3 pens = ₹11

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

• What is the price of pencil & pen

${\large{\sf{\underline{Solution}}}}$

• Let's solve this question by linear equation model. Thus we can get our answer. let's start our solution.

${\underline{ \sf{★ \: Assume\: that,}}}$

${ \bullet{ \sf{ \: \: Pencil \: as \: x}}}$

${ \bullet{ \sf{ \: \: Pen \: as \: y}}}$

${\underline{ \sf{★ \: From \: Question,}}}$

⟾ 2x + 5y = 17 ... equation (1)

⟾ 2x + 3y = 11 ... equation(2)

${\underline{ \sf{★ \: By\: Solving,}}}$

Lets do eq(1) -eq (2)

${\dashrightarrow{\sf{2x + 5y - (2x + 3y) = 17 - 11}}} \\ \\ \\ {\dashrightarrow{\sf{2x + 5y - 2x - 3y = 6}}} \\ \\ \\ {\dashrightarrow{\sf{2y = 6}}} \\ \\ \\ {\dashrightarrow{\sf{y = \frac{6}{2} = 3 }}} \\ \\ \\ { \boxed{ \boxed{ \therefore{ \sf{ \pink{y = 3}}}}}}$

${\underline{ \sf{★ \: By\: Substituting ,}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: {\dashrightarrow{\sf{2x + 5y = 17}}} \\ \\ \\ {\dashrightarrow{\sf{2x + 5 = 17}}} \\ \\ \\ {\dashrightarrow{\sf{2x = 17 - 5}}} \\ \\ \\ {\dashrightarrow{\sf{2x = 12}}} \\ \\ \\ {\dashrightarrow{\sf{x = \frac{12}{2} = 6}}} \\ \\ \\ { \boxed{ \boxed{ \therefore{ \sf{ \pink{x = 6}}}}}}$

$\therefore{\underline{\sf{ \green{Costs \: of \: Pencil \: and \: pen \: are \: 6 Rs \: and \: 3Rs}}}}$