MathematicsThe cost of 4 pens and 4 pencil boxes is Rs 100. Three times the cost of a pen is Rs 15 more than the cost of a pencil box. The cost of a pen and a pencil box respectively are:

The cost of $4$ pens and $4$ pencil boxes is Rs $100$ . Three times the cost of a pen is Rs $15$ more than the cost of a pencil box. The cost of a pen and a pencil box respectively are:

A
Rs $15$ and Rs $8$
B
Rs $10$ and Rs $15$
C
Rs $12$ and Rs $10$
D
Rs $16$ and Rs $12$

Solution:

Given, the cost of

4

pens and

4

pencil boxes is Rs

100

.
Three times the cost of a pen is Rs

15

more than the cost of a pencil box.
Let the cost of a pen and a pencil be Rs

x

and Rs

y

respectively.
⇒

4 x + 4 y = 100

⇒

x + y = 25

...(1)
⇒

3 x = y + 15

⇒

3 x - y = 15

...(2)
Adding (1) and (2), we get,

4 x = 40

⇒

x = 10

Substitute

x = 10

in equation (1) to get,
⇒

y = 15

.
Hence, the correct option is 2.

The cost of $4$ pens and $4$ pencil boxes is Rs $100$ . Three times the cost of a pen is Rs $15$ more than the cost of a pencil box. The cost of a pen and a pencil box respectively are:

Solution:

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