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$5$ pencils and $7$ pens together cost Rs. $50$ whereas $7$ pencils and $5$ pens together cost Rs. $46$ . Thus, the cost of one pencil and one pen respectively is:

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Rs.

5

, Rs.

3

Rs.

3

, Rs.

5

Rs.

4

, Rs.

4

Rs.

2

, Rs.

6

answer is B.

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Detailed Solution

Given the cost of pen and pencil.
Let the cost of one pencil be Rs.

x

and the cost of one pen be Rs.

y

.
According to the first condition,

5 x + 7 y = 50

………(1)

\Rightarrow x = \frac{50 - 7 y}{5}

According to the second condition,

7 x + 5 y = 46

…………..(2)
Substituting

x = \frac{50 - 7 y}{5}

in equation

(2)

\Rightarrow \frac{7 (50 - 7 y)}{5} + 5 y = 46

\Rightarrow 350 - 49 y + 25 y = 230

\Rightarrow y = 5

Substitute the value of

y

to find the value of

x

\Rightarrow x = \frac{50 - 7 (5)}{5}

x = \frac{50 - 35}{5}

\Rightarrow x = 3

∴

Cost of one pencil

=

Rs.

3

and cost of one pen

=

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. Thus, the cost of one pencil and one pen respectively is:

Detailed Solution

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$5$ pencils and $7$ pens together cost Rs. $50$ whereas $7$ pencils and $5$ pens together cost Rs. $46$ . Thus, the cost of one pencil and one pen respectively is: