Question

4 knives and 6 forks cost Rs. 66; 5 knives and 4 forks cost Rs. 72. Find the cost of one knife and one fork.

• A. Rs. 15 and Rs. 7.
• B. Rs. 4 and Rs.9.
• C. Rs. 1 and Rs. 8.
• D. Rs. 12 and Rs. 3.

Answer 1

The correct option is D Rs. 12 and Rs. 3.

Let x rupees and y rupees be the cost of one knife and one fork respectively.
Therefore, according to the question,
$4x+6y=66$ ...(i)
$5x+4y=72$ ...(ii)
On multiplying (i) by 5 and (ii) by 4 and subtracting, we get
$20x+30y=330$
$\underset{–}{\underset{-}{2}0x\underset{-}{+}16y=\underset{-}{2}88}$
$14y=42$
$\therefore y=3$
On putting $y=3$ in (i), we get
$4x+18=66\Rightarrow x=12$
$\therefore \text{cost of one knife=Rs. 12}$ and
$\text{cost of one fork}=Rs.3$