A baker ordered 10 kg of premium flour and some additional kg of standard flour. The price of premium flour per kg was twice that…

Question

A baker ordered 10 kg of premium flour and some additional kg of standard flour. The price of premium flour per kg was twice that of the standard flour. Due to an ordering error, the quantities of the two types of flour were interchanged. This decreased the total cost by 25%. Find the ratio of the quantity of premium flour to standard flour in the original order.

1. A. 1 : 2
2. B. 5 : 2 (Correct answer)
3. C. 3 : 4
4. D. 4 : 5

Correct Answer

Option B — 5 : 2

Detailed Solution & Explanation

The correct answer is 5 : 2.

Key Points

• Let standard flour cost s per kg, so premium costs 2s, and let the standard quantity be x kg.
• Original cost: 10 kg premium + x kg standard = 10(2s) + xs = 20s + xs.
• After the interchange: x kg premium + 10 kg standard = x(2s) + 10s = 2xs + 10s.
• The interchange cut the cost by 25%, so the new cost is 0.75 of the original:
  • 2x + 10 = 0.75(20 + x) = 15 + 0.75x
  • 1.25x = 5 → x = 4
• Premium : standard = 10 : 4 = 5 : 2.

Additional Information

• The unit price s cancels throughout, which is why the answer is a pure ratio and no actual prices are needed.
• Check: with s = 1, original = 20 + 4 = 24 and interchanged = 8 + 10 = 18, and 18/24 = 0.75, a 25% fall ✓.
• Set the cheaper item's price as the base variable and express the other as a multiple of it — that choice keeps the algebra in whole numbers.

प्रश्न (हिन्दी में)

एक बेकर ने 10 किलो प्रीमियम आटा और कुछ अतिरिक्त किलो मानक आटा मंगवाया। प्रति किलो प्रीमियम आटे की कीमत मानक आटे से दोगुनी थी। ऑर्डरिंग त्रुटि के कारण, दो प्रकार के आटे की मात्रा आपस में बदल गई। इससे कुल लागत में 25% की कमी आई। मूल ऑर्डर में प्रीमियम आटे की मात्रा और मानक आटे की मात्रा का अनुपात ज्ञात कीजिए।

1. A. 1 : 2
2. B. 5 : 2
3. C. 3 : 4
4. D. 4 : 5