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Priyanka purchased 2 pencils and 3 erasers for Rs. 9. Sayeeda purchased 1 pencil and two erasers for Rs. 5. What is the cost of one pencil and one eraser?

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The cost of 1 pencil is Rs. 1 and cost of 1 eraser is Rs. 1.

The cost of 1 pencil is Rs. 3 and cost of 1 eraser is Rs. 1.

The cost of 1 pencil is Rs. 1 and cost of 1 eraser is Rs. 3.

The cost of 1 pencil is Rs. 3 and cost of 1 eraser is Rs. 3.

answer is B.

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Detailed Solution

Given that, Priyanka purchased 2 pencils and 3 erasers for Rs. 9. Sayeeda purchased 1 pencil and two erasers for Rs. 5.
We have to find the cost of one pencil and one eraser.
Let the cost of one pencil be Rs. x and cost of one eraser be Rs. y.
Total money spent by Priyanka is Rs. 9 and total money Sayeeda spent = Rs. 5.
Cost of 2 pencils and 3 erasers = Rs. 9
Then,

2 x + 3 y = 9

…(i)
Cost of 1 pencil and 2 erasers = Rs. 5
Then,

x + 2 y = 5

…(ii)
From equation 1

2 x + 3 y = 9 ⇒ 3 y = 9 − 2 x ⇒ y = 9 − 2 x 3 ⇒ y = 9 − 2 x 3 .

Table for

2 x + 3 y = 9

is,

So, points are

0, 3

and

4.5, 0

.
From equation 2

x + 2 y = 5 ⇒ 2 y = 5 − x ⇒ y = 5 − x 2 ⇒ y = 5 − x 2 .

Table for

x + 2 y = 5

is,

So, the points are

0, 2.5

and

5, 0 .

On plotting points

0, 3, 4.5, 0

0, 2.5

and

5, 0

on the graph paper and joining them by a line, we get the following graph for the above equations.

From the graph, it is clear that the two lines intersect at point C (3, 1).
Thus, we get the graphical representation of the given equation.
Therefore, x = 3, y = 1 is the solution of the equations.
Hence, the cost of 1 pencil is Rs 3 and cost of 1 eraser is Rs 1.
Thus, option 2 is correct.

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