The following table shows the total number of air-cooling devices consisting…
2025
The following table shows the total number of air-cooling devices consisting of ACs, Coolers and Fans that were sold by six different stores (A–F), along with the ratio among these devices and the selling price (₹) of these devices per unit. Based on the data in the table, answer the questions that follow.
Store-wise details of air cooling devices
Store | Total Number of Devices Sold | Ratio of Devices AC : Cooler : Fan | Selling Price Per Unit (₹) AC | Cooler | Fan |
|---|---|---|---|---|---|
A | 1250 | 4 : 5 : 1 | 14000 | 4000 | 750 |
B | 450 | 3 : 2 : 4 | 15000 | 4500 | 800 |
C | 850 | 6 : 4 : 7 | 16000 | 5000 | 850 |
D | 900 | 4 : 2 : 3 | 17000 | 5500 | 900 |
E | 1000 | 5 : 1 : 4 | 18000 | 6000 | 950 |
F | 605 | 2 : 4 : 5 | 19000 | 6500 | 1000 |
The number of Fans sold by all the Stores together was
Answer: D. 1650 — Concept When a total is shared among categories in the ratio a : b : c, one part is worth Total ÷ (a + b + c), so the count of any category is Total × (its…
- A.
2050
- B.
1545
- C.
1425
- D.
1650
Show answer & explanation
Correct answer: D
Concept
When a total is shared among categories in the ratio a : b : c, one part is worth Total ÷ (a + b + c), so the count of any category is Total × (its own ratio term) ÷ (a + b + c). Ratio terms belonging to different groups cannot be added or compared directly, because one part is worth a different number of units in each group. A category's overall count is therefore the sum of the counts worked out group by group. Unit prices are irrelevant when only counts are asked for.
Application
For each store, add the three ratio terms to get the number of parts, then take the fan term's share of that store's total.
Store | Devices sold | AC : Cooler : Fan | Ratio parts | Fans = Total × fan term ÷ parts |
|---|---|---|---|---|
A | 1250 | 4 : 5 : 1 | 10 | 1250 × 1 ÷ 10 = 125 |
B | 450 | 3 : 2 : 4 | 9 | 450 × 4 ÷ 9 = 200 |
C | 850 | 6 : 4 : 7 | 17 | 850 × 7 ÷ 17 = 350 |
D | 900 | 4 : 2 : 3 | 9 | 900 × 3 ÷ 9 = 300 |
E | 1000 | 5 : 1 : 4 | 10 | 1000 × 4 ÷ 10 = 400 |
F | 605 | 2 : 4 : 5 | 11 | 605 × 5 ÷ 11 = 275 |
Adding the six store figures: 125 + 200 + 350 + 300 + 400 + 275 = 1650 fans.
Cross-check
Working out the other two categories the same way gives 500 + 150 + 300 + 400 + 500 + 110 = 1960 ACs and 625 + 100 + 200 + 200 + 100 + 220 = 1445 coolers. The three category totals add up to 1960 + 1445 + 1650 = 5055, which is exactly the sum of the Total column (1250 + 450 + 850 + 900 + 1000 + 605 = 5055), confirming the split.
So the six stores together sold 1650 fans.