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In a stationery shop cost of $3$ books $2$ pens and $2$ pencils all together is Rs. $129$ . Cost of $1$ book $2$ pens and $2$ pencils together is Rs. $79$ . And cost of $1$ book and $1$ pencil together is Rs. $2$ $0$ . If Ajinkya buys $2$ $1$ books, $2$ pencils and $3$ pens. How much will he pay to the shopkeeper? $\newline$ ( $1$ ) Rs $2$ $4$ $\newline$ ( $2$ ) Rs $2$ $5$ $\newline$ ( $3$ ) Rs $2$ $6$ $\newline$ ( $4$ ) Rs $2$ $7$

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Q. In a stationery shop cost of

3

books

2

pens and

2

pencils all together is Rs.

129

. Cost of

1

book

2

pens and

2

pencils together is Rs.

79

. And cost of

1

book and

1

pencil together is Rs.

2

0

. If Ajinkya buys

2

1

books,

2

pencils and

3

pens. How much will he pay to the shopkeeper?

\newline

(

1

) Rs

2

4

\newline

(

2

) Rs

2

5

\newline

(

3

) Rs

2

6

\newline

(

4

) Rs

2

7

Equations Denotation: Let's denote the cost of one book as $B$ , the cost of one pen as $P$ , and the cost of one pencil as $C$ . We are given three equations based on the information provided: $\newline$ $1$ . For $3$ books, $2$ pens, and $2$ pencils: $3B + 2P + 2C = 129$ $\newline$ $2$ . For $1$ book, $2$ pens, and $2$ pencils: $P$ $0$ $\newline$ $3$ . For $1$ book and $1$ pencil: $P$ $3$ $\newline$ We will use these equations to find the values of $B$ , $P$ , and $C$ .
Find Cost of $1$ Pen: First, we will subtract the third equation from the second equation to find the cost of $1$ pen. $\newline$ $(B + 2P + 2C) - (B + C) = 79 - 37$ $\newline$ $2P + C = 42$ $\newline$ Since we know $B + C = 37$ from the third equation, we can substitute $C$ from the third equation into the new equation: $\newline$ $2P + (37 - B) = 42$ $\newline$ $2P + 37 - B = 42$ $\newline$ $2P = 42 - 37 + B$ $\newline$ $2P = 5 + B$
Find Cost of $2$ Books: Now, we will subtract the second equation from the first equation to find the cost of $2$ books. $\newline$ $(3B + 2P + 2C) - (B + 2P + 2C) = 129 - 79$ $\newline$ $2B = 50$ $\newline$ Dividing both sides by $2$ gives us the cost of one book: $\newline$ $B = 25$
Find Cost of $1$ Pen: Now that we have the value of $B$ , we can find the value of $P$ by substituting $B$ into the equation $2P = 5 + B$ . $2P = 5 + 25$ $2P = 30$ Dividing both sides by $2$ gives us the cost of one pen: $P = 15$
Find Cost of $1$ Pencil: We can now find the value of $C$ by substituting the value of $B$ into the third equation $B + C = 37$ . $\newline$ $25 + C = 37$ $\newline$ Subtracting $25$ from both sides gives us the cost of one pencil: $\newline$ $C = 37 - 25$ $\newline$ $C = 12$
Calculate Total Cost: Now that we have the costs of a book, a pen, and a pencil $B = 25$ , $P = 15$ , $C = 12$ , we can calculate the total cost for Ajinkya's purchase of $4$ books, $2$ pencils, and $3$ pens. $\newline$ Total cost = $4B + 2C + 3P$ $\newline$ Total cost = $4(25) + 2(12) + 3(15)$ $\newline$ Total cost = $100 + 24 + 45$ $\newline$ Total cost = $169$