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?
- (a)1:2
- (b)2:1
- (c)5:2
- (d)2:5
Answer
Why
Correct — D. Let a desktop cost p, so a laptop costs 5p, and let the order have d desktops.
Ordered bill = 20 × 5p + d × p = (100 + d)p
Delivered bill, counts swapped = d × 5p + 20 × p = (5d + 20)p
Delivered = 1.8 × ordered:
5d + 20 = 180 + 1.8d
3.2d = 160, so d = 50
Laptops : desktops = 20 : 50 = 2 : 5 → option (d)
Check: the bill goes from 150p to 270p, and 270 ÷ 150 = 1.8.
Why the others are wrong
- (a)1:2 — 1 : 2 means 40 desktops. The bill would go from 140p to 220p, a rise of 80p on 140p, about 57%, not 80%.
- (b)2:1 — 2 : 1 means 10 desktops, fewer than the 20 laptops. The swap would deliver 10 laptops and 20 desktops, cutting the bill from 110p to 70p instead of raising it.
- (c)5:2 — 5 : 2 means 8 desktops. With more laptops than desktops ordered, the swap cuts the bill from 108p to 60p, when the stem says it rose 80%.
Concept
When the counts of two items are interchanged, the bill rises only if more of the expensive item arrives than was ordered. So the original order had fewer laptops than desktops, which rules out 2 : 1 and 5 : 2 before any arithmetic.
To solve, write both bills with one unknown count and one unit price, set delivered = 1.8 × ordered, and solve the linear equation. The unit price p cancels.
Swapping changes this bill by (5d + 20)p − (100 + d)p = 4(d − 20)p, which is positive only when d is above 20. Setting 4(d − 20) equal to 80% of (100 + d) gives d = 50 again.
Key facts
- A rise of 80% means the new bill is 1.8 × the old bill.
- Here the swap changes the bill by 4(d − 20)p, so it rises only when d > 20.
- The original order was 20 laptops and 50 desktops.
Study next
Common traps
- Finding d = 50 correctly and then writing the ratio the wrong way round as 5 : 2.
- Reading 'increase by 80%' as the new bill being 80% of the old, which would make the bill fall.
The same swap structure appears at 14 Sep 2025, 16:00, Quant Q.8 (red and blue pens, red priced at 3× blue, bill up 40%). Interchanged counts of ₹20 and ₹10 notes are asked at 23 Sep 2024, 09:00, Quant Q.9.
Related PYQs
No directly related past PYQ was found.