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
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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
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
(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