Correct Answer - Option 4 : 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.