If the price of an article is increased by Rs 2 per dozen than at pres

1.	If the price of an article is increased by Rs 2 per dozen than at present, the number of things available for Rs 56 is 8 less than before. The price per dozen at present is : (a) Rs 14 (b) Rs 12 (c) Rs 10 (d) Rs 28
Answer» (b) Rs 12 Let the present price be Rs k per dozen. ∴ Price per unit = Rs \(\frac{k}{12}\) ∴ Increased price = Rs (k +2) per dozen ∴ Increase price per unit = Rs \(\frac{(k+2)}{12}\) Given, \(\frac{56}{\frac{k}{12}}-\frac{56}{\frac{(k +2)}{12}} = 8\) ⇒ \(\frac{12\times56}{k}-\frac{12\times56}{k+2}=8\) ⇒ 672 x (k + 2) - 672k = 8k(k + 2) ⇒ 8k² + 16k - 1344 = 0 ⇒ k² + 2k - 168 = 0 ⇒ (k + 14)(k - 12) = 0 ⇒ k = 12

If the price of an article is increased by Rs 2 per dozen than at present, the number of things available for Rs 56 is 8 less than before. The price per dozen at present is : (a) Rs 14 (b) Rs 12 (c) Rs 10 (d) Rs 28

Answer»

(b) Rs 12

Let the present price be Rs k per dozen.

∴ Price per unit = Rs \(\frac{k}{12}\)

∴ Increased price = Rs (k +2) per dozen

∴ Increase price per unit = Rs \(\frac{(k+2)}{12}\)

Given, \(\frac{56}{\frac{k}{12}}-\frac{56}{\frac{(k +2)}{12}} = 8\)

⇒ \(\frac{12\times56}{k}-\frac{12\times56}{k+2}=8\)

⇒ 672 x (k + 2) - 672k = 8k(k + 2)

⇒ 8k² + 16k - 1344 = 0

⇒ k² + 2k - 168 = 0 ⇒ (k + 14)(k - 12) = 0

⇒ k = 12