Question : The cost of 3 cups and 5 plates is INR 1,080 and the cost of 2 cups and 4 plates is INR 840. Find the ratio of the cost of a cup to the cost of a plate.
Option 1: 1 : 3
Option 2: 2 : 3
Option 3: 1 : 1
Option 4: 1 : 2
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Correct Answer: 1 : 3
Solution :
Let the cost of 1 cup be $x$ and the cost of 1 plate be $y$>
So, according to the question, the equations formed are
3$x$ + 5$y$ = 1080............(equation 1)
And, 2$x$ + 4$x$ = 840.............(equation 2)
Multiplying equation 1 by 2 and equation 2 by 3, we get:
6$x$ + 10$y$ = 2160................(equation 3)
6$x$ + 12$y$ = 2520.................(equation 4)
Subtract equation 3 from equation 4, we get:
2$y$ = 360
⇒ $y$ = 180
Putting the value of plates in equation 1, we get:
3$x$ + 5 × 180 = 1080
⇒ $x$ = 60
$\therefore$ Ratio of the cost of a cup to the cost of a plate = 60 : 180 = 1 : 3
Hence, the correct answer is 1 : 3.
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