$5$ pen and $6$ pencils together cost $Rs.9$ and $3$ pens and 2 pencils cost $Rs.5$. Find the cost of $1$ pen and $1$ pencil.
Last updated date: 17th Mar 2023
•
Total views: 305.7k
•
Views today: 5.84k
Answer
305.7k+ views
Hint:In order to solve these types of questions, firstly we have to convert the statements into equations by which we get two equations and after solving these equations we will get the cost of $1$ pen and $1$ pencil.
Complete step-by-step answer:
Assuming,
The cost of a pen be $Rs.x$ and that of pencil be $Rs.y$
We have given that, cost of $5$ pen and $6$ pencils together cost $Rs.9$
Therefore,
$5x + 6y = 9 - - - - - - \left( 1 \right)$
And the cost of $3$ pens and 2 pencils cost $Rs.5$.
Thus,
$3x + 2y = 5 - - - - - - \left( 2 \right)$
Multiplying equation (1) by 2 and equation (2) by 6, we get
$10x + 12y = 18 - - - - - \left( 3 \right)$
$18x + 12y = 30 - - - - - \left( 4 \right)$
Subtracting equation (3) by equation (4), we get
$18x - 10x + 12y - 12y = 30 - 18$
Or $8x = 12$
Or $x = \dfrac{3}{2}$
Or $x = 1.5$
Substituting $x = 1.5$
In equation (1), we get
$5 \times 1.5 + 6y = 9$
Or $7.5 + 6y = 9$
Or $6y = 9 - 7.5$
Or $6y = 1.5$
Or $y = \dfrac{{1.5}}{6}$
Or $y = \dfrac{1}{4}$
Or $y = 0.25$
Hence, the cost of one pen $ = Rs1.50$ and the cost of one pencil $ = Rs0.25$ .
Note: Whenever we face such a type of question simply we have to assume the cost Assume the cost of a pen be $Rs.x$ and that of pencil be $Rs.y$ after then we have to solve the equations by adding or subtracting equations to get our desired answer.
Complete step-by-step answer:
Assuming,
The cost of a pen be $Rs.x$ and that of pencil be $Rs.y$
We have given that, cost of $5$ pen and $6$ pencils together cost $Rs.9$
Therefore,
$5x + 6y = 9 - - - - - - \left( 1 \right)$
And the cost of $3$ pens and 2 pencils cost $Rs.5$.
Thus,
$3x + 2y = 5 - - - - - - \left( 2 \right)$
Multiplying equation (1) by 2 and equation (2) by 6, we get
$10x + 12y = 18 - - - - - \left( 3 \right)$
$18x + 12y = 30 - - - - - \left( 4 \right)$
Subtracting equation (3) by equation (4), we get
$18x - 10x + 12y - 12y = 30 - 18$
Or $8x = 12$
Or $x = \dfrac{3}{2}$
Or $x = 1.5$
Substituting $x = 1.5$
In equation (1), we get
$5 \times 1.5 + 6y = 9$
Or $7.5 + 6y = 9$
Or $6y = 9 - 7.5$
Or $6y = 1.5$
Or $y = \dfrac{{1.5}}{6}$
Or $y = \dfrac{1}{4}$
Or $y = 0.25$
Hence, the cost of one pen $ = Rs1.50$ and the cost of one pencil $ = Rs0.25$ .
Note: Whenever we face such a type of question simply we have to assume the cost Assume the cost of a pen be $Rs.x$ and that of pencil be $Rs.y$ after then we have to solve the equations by adding or subtracting equations to get our desired answer.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
