Directions : Read the following bar graphs carefully and answer the questions…
2024
Directions : Read the following bar graphs carefully and answer the questions given below. The bar graphs shows discount percentage given on marked price of four different items in 2022 and 2024.
Note: (i) The marked price of an item can be same or different in both years.
(ii) The cost price of an item can be same or different in both the years.
The ratio of the selling price of items R and S in 2024 is 2:5 and the profit on selling items R and S in 2024 is 20% and 25% respectively. Find the cost price of item R is what percentage of the cost price of item S in 2024.
- A.
43.33%
- B.
49.25%
- C.
42.83%
- D.
44.5%
- E.
41.67%
Attempted by 1 students.
Show answer & explanation
Correct answer: E
Concept
For any item, Selling Price = Cost Price x (1 + Profit fraction), so Cost Price = Selling Price / (1 + Profit fraction). When you know the ratio of selling prices and the profit rate of each item, the ratio of cost prices is obtained by dividing each selling price by its own (1 + Profit fraction) factor.
Application
Let the selling prices in 2024 be SP(R) = 2k and SP(S) = 5k, using the given ratio 2 : 5.
Item R earns a 20% profit, so CP(R) = 2k / 1.20 = 2k / (6/5) = (5/3)k.
Item S earns a 25% profit, so CP(S) = 5k / 1.25 = 5k / (5/4) = 4k.
Required percentage = CP(R) / CP(S) x 100 = (5/3)k / 4k x 100 = 5/12 x 100 = 41.67% (to 2 decimal places).
Cross-check
CP(R) : CP(S) = (5/3) : 4 = 5 : 12. Then 5 / 12 = 0.41666..., which is 41.67% after rounding to two decimals, confirming the result. Notice the answer is below the raw 2 : 5 = 40% because S's higher profit rate shrinks its cost price more than R's, nudging the cost-price ratio upward from 40%.