Directions : Read the following table carefully and answer the questions given…
2022
Directions : Read the following table carefully and answer the questions given below.
Two shops X & Y sell two (R & T) different articles and each article is marked up and then sold after giving a certain discount. Table shows the cost price, marked price and relation between ‘a’ & ‘b’ variables for both shops and the discount given by them at different times.
Note: Relationship between ‘a’ & ‘b’ variable for both shops are different.
Articles | Cost price (Rs.) | Marked price (Rs.) |
|---|---|---|
R | 5000 + a | 12b |
T | 8000 + a | 25b |
Shops | Relation between a & b |
|---|---|
X | a = 3b |
Y | 3a = 10b |
Timing | Discount offered by both shops (Rs.) |
|---|---|
1:30 pm | a/5 |
2:30 pm | b/5 |
3:30 pm | (a+b)/5 |
The profit percentage earned by shop X on selling article R at 1:30 pm is 42.5%. Find the profit percentage by the same shop on selling the article T at 2:30 pm.
- A.
125.45%
- B.
110.50%
- C.
92.33%
- D.
87.50%
- E.
115.25%
Attempted by 1 students.
Show answer & explanation
Correct answer: A
Concept
Selling Price (SP) = Marked Price (MP) − Discount, and Profit% = (SP − CP) ÷ CP × 100. When unknowns appear in CP, MP and the discount, first pin them down using the one fully-known profit figure, then reuse those numbers for the asked item.
Application
For Shop X the relation is a = 3b. For article R: CP = 5000 + a, MP = 12b, and the 1:30 pm discount is a/5.
SP of R = 12b − a/5 = 12b − 3b/5 = 57b/5 (after putting a = 3b).
Given profit on R = 42.5%, so (57b/5 − (5000 + 3b)) ÷ (5000 + 3b) = 0.425.
Multiply both sides by (5000 + 3b): 57b/5 − 5000 − 3b = 0.425 × (5000 + 3b) = 2125 + 1.275b.
Collect the b terms: 57b/5 − 3b − 1.275b = 7125, i.e. (11.4 − 3 − 1.275)b = 7125, so 7.125b = 7125.
Solve for b: b = 7125 ÷ 7.125 = 1000, hence a = 3b = 3000.
Now for article T sold by Shop X at 2:30 pm: CP = 8000 + a = 8000 + 3000 = 11000; MP = 25b = 25000; the 2:30 pm discount is b/5 = 1000/5 = 200.
SP of T = 25000 − 200 = 24800.
Profit% on T = (24800 − 11000) ÷ 11000 × 100 = 13800 ÷ 11000 × 100 = 1380/11 = 125.45% (approx).
Cross-check
Verify the derived values on R: CP = 5000 + 3000 = 8000, SP = 12(1000) − 3000/5 = 12000 − 600 = 11400, profit% = (11400 − 8000)/8000 × 100 = 42.5%, matching the given figure. So a = 3000, b = 1000 are correct, and T yields 125.45%.