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 |
Shop Y sold article T at 3:30 pm at a profit of Rs. (2a+b-120). If difference between the price by which articles R & T were marked up by shop Y is ‘C’, then which of the following statement/s is/are correct?
(A) 7b < C < 3a - b + 2150
(B) 2a + b < C < 3a - 2b + 3250
(C) 3a - b + 2000 > C > 8b + 1050
- A.
Only (A) & (C)
- B.
Only (A) & (B)
- C.
Only (B) & (C)
- D.
Only (A)
- E.
Only (B)
Attempted by 1 students.
Show answer & explanation
Correct answer: B
Concept
In mark-up/discount problems, the markup of an article is the amount added to its cost price to reach the marked price: Markup = Marked Price - Cost Price. The selling price under a discount is SP = MP - Discount, and Profit = SP - CP. To compare two articles' markups, compute each markup separately and take the difference.
Setting up the variables (Shop Y)
For Shop Y the stated relation is 3a = 10b, i.e. a = (10/3)*b. We first pin down a and b using the profit fact, then evaluate every inequality with concrete numbers.
Application - step by step
Write the profit equation for article T at 3:30 pm. Discount at 3:30 pm = (a + b)/5, MP of T = 25b, CP of T = 8000 + a. So Profit = MP - Discount - CP = 25b - (a + b)/5 - (8000 + a).
Equate to the given profit (2a + b - 120): 25b - (a + b)/5 - (8000 + a) = 2a + b - 120.
Clear the fraction (multiply by 5) and simplify to 119b - 16a - 39400 = 0.
Substitute a = (10/3)*b: 119b - (160/3)b = 39400, so (197/3)b = 39400, giving b = 600 and then a = (10/3)*600 = 2000.
Compute the two markups for Shop Y. Markup of R = 12b - (5000 + a) = 7200 - 7000 = 200. Markup of T = 25b - (8000 + a) = 15000 - 10000 = 5000.
Therefore C = |Markup_T - Markup_R| = |5000 - 200| = 4800.
Cross-check the three statements (a = 2000, b = 600, C = 4800)
(A) 7b < C < 3a - b + 2150 gives 4200 < 4800 < 7550. Both bounds hold, so A is correct.
(B) 2a + b < C < 3a - 2b + 3250 gives 4600 < 4800 < 8050. Both bounds hold, so B is correct.
(C) 3a - b + 2000 > C > 8b + 1050 gives 7400 > 4800 > 5850. The lower bound fails because 4800 is not greater than 5850, so C is incorrect.
Result
Statements A and B hold while C does not, so the correct choice is Only (A) & (B).
Independent check of b: with a = 2000, b = 600, SP of T = 25*600 - 2600/5 = 15000 - 520 = 14480 and CP of T = 10000, giving profit 4480 = 2(2000) + 600 - 120. The values are consistent.