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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.37. If Ajinkya buys 4 books, 2 pencils and 3 pens. How much will he pay to the shopkeeper?
(A) Rs 31
(B) Rs 150
(C) Rs 189
(D) Rs 169

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. $37$ . If Ajinkya buys $4$ books, $2$ pencils and $3$ pens. How much will he pay to the shopkeeper? $\newline$ (A) Rs $31$ $\newline$ (B) Rs $150$ $\newline$ (C) Rs $189$ $\newline$ (D) Rs $169$

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Finance problems

Full solution

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.

37

. If Ajinkya buys

4

books,

2

pencils and

3

pens. How much will he pay to the shopkeeper?

\newline

(A) Rs

31

\newline

(B) Rs

150

\newline

(C) Rs

189

\newline

(D) Rs

169

Equations Setup: 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, the cost is Rs. $129$ . $\newline$ $2$ . For $1$ book, $2$ pens, and $2$ pencils, the cost is Rs. $P$ $0$ . $\newline$ $3$ . For $1$ book and $1$ pencil, the cost is Rs. $P$ $3$ . $\newline$ We can write these equations as: $\newline$ $P$ $4$ ...( $1$ ) $\newline$ $P$ $6$ ...( $2$ ) $\newline$ $P$ $8$ ...( $3$ ) $\newline$ Now, we will solve these equations to find the values of $B$ , $P$ , and $C$ .
Calculate Cost of Book: First, we will subtract equation ( $2$ ) from equation ( $1$ ) to find the cost of $2$ books: $\newline$ $(3B + 2P + 2C) - (B + 2P + 2C) = 129 - 79$ $\newline$ $2B = 50$ $\newline$ $B = 25$ $\newline$ So, the cost of one book is Rs. $25$ .
Calculate Cost of Pencil: Next, we will substitute the value of $B$ into equation ( $3$ ) to find the cost of one pencil: $\newline$ $B + C = 37$ $\newline$ $25 + C = 37$ $\newline$ $C = 37 - 25$ $\newline$ $C = 12$ $\newline$ So, the cost of one pencil is Rs. $12$ .
Calculate Cost of Pen: Now, we will substitute the values of $B$ and $C$ into equation $(2)$ to find the cost of two pens: $\newline$ $B + 2P + 2C = 79$ $\newline$ $25 + 2P + 2(12) = 79$ $\newline$ $25 + 2P + 24 = 79$ $\newline$ $2P = 79 - 25 - 24$ $\newline$ $2P = 30$ $\newline$ $P = 15$ $\newline$ So, the cost of one pen is Rs. $15$ .
Total Cost Calculation: Finally, we will calculate the total cost for Ajinkya, who buys $4$ 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 = $169$ $\newline$ So, Ajinkya will pay Rs. $169$ to the shopkeeper.

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