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$5$ pencils and $7$ pens together cost Rs. $50$ , whereas $7$ pencils and $5$ pens together cost Rs. $46$ . Find the cost of one pencil and that of one pen by graphical method.

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Cost of one pencil

=

Rs.

2

and that of one pen

=

Rs.

4

Cost of one pencil

=

Rs.

3

and that of one pen

=

Rs.

5

Cost of one pencil

=

Rs.

5

and that of one pen

=

Rs.

6

Cost of one pencil

=

Rs.

2

and that of one pen

=

Rs.

6

answer is B.

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Detailed Solution

Given a pencil and pen.
Let cost of pencil be Rs.

x

and cost of pens be Rs.

y

5

pencils and

7

pens together cost Rs.

50

,
So we get,

5 x + 7 y = 50

5 x = 50 - 7 y

x = 10 - \frac{7}{5} y

Let’s take

y = 5

x = 10 - \frac{7}{5} y

x = 10 - 7

x = 3

Let’s take

y = 10

x = 10 - \frac{7}{5} y

x = 10 - 14

x = - 4

Therefore, the required points are

(3, 5), (- 4, 10)

.
Also, given that

7

pencils and

5

pens together cost Rs.

46

7 x + 5 y = 46

5 y = 46 - 7 x

y = 9.2 - 1.4 x

Let’s take

x = 0

y = 9.2 - 0

y = 9.2

Let’s take

x = 2

y = 9.2 - 2.8

y = 6.4

Therefore, the required points are

(0, 9.2), (2, 6.4)

.
The graph is as shown below:
Question Image

Since the point of intersection is

(3, 5),

thus the cost of one pencil is Rs.

3

and the cost of one pen is Rs.

5

.
Therefore, option (2) is correct.

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5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and that of one pen by graphical method.

Detailed Solution

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$5$ pencils and $7$ pens together cost Rs. $50$ , whereas $7$ pencils and $5$ pens together cost Rs. $46$ . Find the cost of one pencil and that of one pen by graphical method.