Question

It 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 1

Answer: (B)

Rs. $12$

Let the present price be Rs. $K$ per dozen.

$\therefore$ Price per unit Rs $\frac{k}{12}$

$\therefore$ Increased price $=Rs.(k+2)$ per dozen

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

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

$\Rightarrow \frac{12\times 56}{k}-\frac{12\times 56}{k+2}=8$

$\Rightarrow 672\times (k+2)-672k=8k(k+2)$

$(81{)}^{{}^2}+11344=0$

$\Rightarrow k^2+2k-168=0$

$\Rightarrow (k+14)(k-12)=0\Rightarrow k=12$