Question: A man buys a few number of books at Rs 72 each and a few number of pens at Rs 25 each. If he buys 11 articles and pays Rs 510 altogether, find the number of each article bought by him.

Solution:

Let the total number of books bought be 'x' and the total number of pens bought be 'y'.

Then, total money spent on books = Rs 72x

Total money spent on pens = Ra 25y

According to the question,

The man bought 11 articles.
or, x + y = 11
or, x = 11 - y - (i)

He paid Rs 510 altogether,

or, 72x + 25y = 510

[Put value of x from equation (i) ]

or, 72(11 -y) + 25 y = 510

or, 792 - 72 y +25y = 510

or, 792 - 510 - 47y = 0

or, 47y = 282

or, y = \dfrac{282}{47}

\therefore y = 6

And,

Put value of y in equation (i), we get,

or, x = 11 - 6

\therefore x = 5

So, (x,y) = (5,6)

Therefore, the required of books bought by the man was 5 and the number of pens bought was 6.