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The cost price of an item is Rs Q and it was marked up on its cost price by R%. A discount of S% was provided while selling the item such that the percentage profit earned in selling it was 12.5% and the profit earned was Rs 45. If the article had been sold at a mark-up of (4R/5)% on the cost price and discount provided was R%, there would have been a loss of Rs 36. Which of the following can be determined? (A) The value of Q (B) The value of R (C) The value of S (D) Initial profit if the item had been sold without providing discount.

The cost price of an item is Rs Q and it was marked up on its cost price by R%. A discount of S% was provided while selling the item such that the percentage profit earned in selling it was 12.5% and the profit earned was Rs 45. If the article had been sold at a mark-up of (4R/5)% on the cost price and discount provided was R%, there would have been a loss of Rs 36. Which of the following can be determined? (A) The value of Q (B) The value of R (C) The value of S (D) Initial profit if the item had been sold without providing discount. Correct Answer All A, B, C and D

S.P of the item = Rs (Q + 45)

So, ((Q + 45) – Q)/Q) × 100% = 12.5%

⇒ 45/Q = 0.125

⇒ Q = 360

S.P of the item = Rs. 405

M.P of the item = Rs. 360(1 + R/100)

S.P of the item = Rs 360(1 + R/100)(1 – S/100)

So, 360 (1 + R/100)(1 – T/100) = 405

⇒ (1 + R/100)(1 – S/100) = 9/8 ----(i)

In new scenario :

S.P of the item = 360(1 + (4R/5)/100) (1 – R/100)

Since, there is a loss of Rs 36, S.P = 360 – 36 = 324

So, 360(1 + (4R/5)/100) (1 – R/100) = 324

Let R/100 = x

So, (1 + 4x/5) (1 – x) = 9/10

⇒ 1 – x + 4x/5 – 4x2/5 = 9/10

⇒ 10 – 10x + 8x – 8x2 = 9

⇒ 8x2 + 2x – 1 = 0

⇒ (2x + 1) (4x – 1) = 0

⇒ x = -1/2 or ¼

If x = -1/2, R = -50, but the percentage markup cannot be negative,

So, x = ¼, B = 25

Putting in (i)

(1 + ¼)(1 – S/100) = 9/8

⇒ 1 – S/100 = 9/10

⇒ C = 10

S.P of the item if it was sold without discount =

360 × (125/100) = Rs 90

So, all (Q), (R), (S) and (T) are determined.

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