if the cost of pins reduces by Rs.4 per dozen. 12 more pins can be purchased for Rs.48. The cost of pins per dozen after reduction is:

if the cost of pins reduces by Rs.4 per dozen. 12 more pins can be purchased for Rs.48. The cost of pins per dozen after reduction is:
1). Rs.8
2). Rs.12
3). Rs.16
4). Rs.20

Let the original cost of pins per dozen be Rs. x.

Since the price reduces by Rs. 4 per dozen and 12 more pins (which is 1 dozen) can be bought for Rs. 48, the difference in the number of dozens before and after the reduction is 1.

Using the relation:

48 / (x - 4) - 48 / x = 1

Step 1: Find a common denominator:
48(x - x + 4) / [x(x - 4)] = 1

Step 2: Simplify:
192 / [x(x - 4)] = 1

Step 3: Cross-multiply:
192 = x(x - 4)
x² - 4x - 192 = 0

Step 4: Factor the quadratic:
(x - 16)(x + 12) = 0

So, x = 16 (since cost cannot be negative).

After the reduction, the cost per dozen is:
16 - 4 = 12

Final Answer: Rs. 12

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