A company placed an order for 20 high-end laptops and some quantity of standard desktops. The price of a high-end laptop was 5 ti…

Question

A company placed an order for 20 high-end laptops and some quantity of standard desktops. The price of a high-end laptop was 5 times that of a standard desktop. Due to a mistake, the number of laptops and desktops was interchanged in the delivery. This caused the total bill to increase by 80%. What was the ratio of the number of high-end laptops to standard desktops in the original order?

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

Correct Answer

Option D — 2:5

Detailed Solution & Explanation

The correct answer is 2:5.

Key Points

• Let a desktop cost p, so a laptop costs 5p, and let there be d desktops.
• Original bill $= 20(5p) + dp = 100p + dp$. After the interchange: $d(5p) + 20p = 5dp + 20p$.
• The interchange raised the bill by 80%, so $5d + 20 = 1.8(100 + d)$, giving $3.2d = 160$ and d = 50.
• The original ratio of laptops to desktops is $20 : 50 = $ 2 : 5.

Additional Information

• The unit price p cancels out entirely, which is the signal that only the ratio was ever recoverable — the question could not have asked for actual prices.
• Check it: original $= 100p + 50p = 150p$; interchanged $= 250p + 20p = 270p$; and $270/150 = 1.8$ ✓
• 5 : 2 is offered as the reversal trap — read carefully which quantity the ratio is asked for first.

प्रश्न (हिन्दी में)

एक कंपनी ने 20 हाई-एंड लैपटॉप और कुछ मात्रा में स्टैंडर्ड डेस्कटॉप का ऑर्डर दिया। हाई-एंड लैपटॉप की कीमत स्टैंडर्ड डेस्कटॉप से 5 गुना थी। एक गलती के कारण, डिलीवरी में लैपटॉप और डेस्कटॉप की संख्या आपस में बदल गई। इससे कुल बिल 80% बढ़ गया। मूल ऑर्डर में हाई-एंड लैपटॉप और स्टैंडर्ड डेस्कटॉप की संख्या का अनुपात क्या था?

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