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If $7$ pens and $3$ books cost $Rs . 1395$ , while $5$ pens and $4$ books cost $Rs . 1665$ . Find the cost of a book.

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Rs.

360

Rs.

45360

Rs.

35350

None

answer is A.

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Detailed Solution

It is given

7

pens and

3

books cost

Rs . 1395

, while

5

pens and

4

books cost

Rs . 1665

.
Let the cost of

1

pen be

x

and the cost of

1

book be

y .

Then,

7 x + 3 y = 1395

-----

(1)

5 x + 4 y = 1665 - - (2)

Now multiplying the equation (1) with 4 we get,

4 (7 x + 3 y) = 4 \times 1395

28 x + 12 y

= 5580…(3).
Also multiplying theequation (2) with 3 we get,

3 (5 x + 4 y) = 3 \times 1665

15 x + 12 y

= 4995…(4)
Now, subtracting the equation (4) from the equation (3) we get,

(28 x + 12 y) - (15 x + 12 y) = 5580 - 4995

28 x - 15 x = 585

13 x = 585

x = 45

Putting

x = 45

in equation (1) we get,

7 \times 45 + 3 y = 1395

\Rightarrow 315 + 3 y = 1395

\Rightarrow 3 y = 1395 - 315

\Rightarrow 3 y = 1080

\Rightarrow y = \frac{1080}{3}

\Rightarrow y = 360

So the cost of one book is Rs

360

.
So the correct option is 1.

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