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If the cost of pins reduces by $ 4 per dozen, 12 more pins can be purchased for $ 48. The cost of pins per dozen after reduction is:
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- $ 8
- $ 12
- $ 16
- $ 20
Correct Option: B
Let the original price = y per dozen
New price = (y – 4) per dozen
| Original number of pins = | dozens | y |
| New number of pins = | dozens | y - 4 |
According to the question,
| - | = 1 | y - 4 | y |
| ⇒ 48 |  | y - y + 4 |  | = 1 | ||
| y(y - 4) |
⇒ y (y – 4) = 48 × 4
⇒ y 2 – 4y – 192 = 0
⇒ y 2 – 16y + 12y – 192 = 0
⇒ y(y – 16) + 12 (y – 16) = 0
⇒ (y – 16) (y + 12) = 0
⇒ y = 16, because the price of pins can not be negative.
∴ y ≠ –12
∴ New price = 16 – 4 = $ 12 per dozen
