A reduction of 10% in the price of a pen enabled a trader to purchase 9 more…

When the price of an item is reduced by a fixed percentage but the total amount spent stays the same, the quantity bought rises in inverse proportion to the price. Writing the number of items as Total amount / Price, both before and after the reduction, turns the extra-quantity condition into one equation in the original price.

1. Let the original price of one pen be x (in Rs).

2. Number of pens bought for Rs 540 at the original price = 540/x.

3. After a 10% reduction, the new price = 9x/10.

4. Number of pens bought for Rs 540 at the reduced price = 540 divided by (9x/10) = 600/x.

5. Extra pens purchased because of the reduction = 600/x minus 540/x = 60/x.

6. This extra quantity is given as 9, so solving 60/x = 9 gives x = 60/9 = 20/3.

7. Reduced price = (9/10) times x = (9/10) times (20/3) = 6.

Check: at the original price x = 20/3, the trader buys 540 divided by (20/3) = 81 pens; at the reduced price, he buys 540/6 = 90 pens, exactly 9 more, confirming the value.