Question

Rohan ordered 5 kg of premium coffee and some additional kilograms of ordinary coffee. The price of the premium coffee per kg was three times that of the ordinary coffee. When the order was delivered, it was found that the quantities of premium and ordinary coffee had been swapped. This change increased his bill by 40%. Find the ratio of the original quantity of premium coffee to the original quantity of ordinary coffee.

• A. 2 : 1
• B. 1 : 3
• C. 1 : 2
• D. 3 : 1

Answer 1

Answer:

C. 1 : 2

Let the price of ordinary coffee be ₹x per kg.

Then the price of premium coffee = ₹3x per kg.

Original order

• Premium coffee = 5 kg

• Ordinary coffee = (y) kg

Original bill:

5(3x) + y(x) = x(15+y)

Delivered order (quantities swapped)

• Premium coffee = (y) kg

• Ordinary coffee = 5 kg

New bill:

y(3x) + 5(x) = x(3y+5)

The bill increased by 40%, so:

x(3y+5)=1.4,x(15+y)

Cancel (x):

3y+5=1.4(15+y)
3y+5=21+1.4y
1.6y=16
y=10

So the original quantities were:

• Premium coffee = 5 kg

• Ordinary coffee = 10 kg

Therefore, the required ratio is

5:10 = 1:2

$Answer: (\boxed{1:2}).$