Question

when a pen is sold at a discount of 15%.There is a gain of rs 10.But if it is sold at 25% discount there is a loss of rs 2.Find the Mark price of the pen.​

Answer 1

Mark Price: RS. 120

The Gain Function is the difference between Resulting Price, which is the Mark Price including Discount Rate, and the Reference Price, where positive result represents Net Gain, as negative result represents Net Loss. Gain Function is described below:

$G = \left(1-\frac{r_{D}}{100} \right)\cdot P_{M}-P_{R}$ (1)

Where:

$G$ - Gain function, in monetary units.

$r_{D}$ - Discount rate, in percentage.

$P_{M}$ - Mark price, in monetary units.

$P_{R}$ - Reference price, in monetary units.

The Mark Price of the pen is the price shown on the label of the product, whereas the Reference Price is the purchase cost of the product from provider.

Based on what it is written on statement we have the following system of linear equations:

1) When a pen is sold at a discount of 15 %. There is a gain of RS. 10: ($G = 10$, $r_{D} = 15$)

$\left(1-\frac{15}{100} \right)\cdot P_{M} - P_{R} = 10$ (2)

2) But if it is sold at 25 % discount there is a loss of RS. 2: ($G = -2$, $r_{D} = 25$)

$\left(1-\frac{25}{100} \right)\cdot P_{M} - P_{R} = -2$ (3)

The solution of the resulting system of linear equations is:

$P_{M} = 120$, $P_{R} = 92$

The mark price of the pen is RP. 120.

Answer 2

When a pen is sold at a discount of 15% there is a gain of rs 10

When the pen is sold at 25% discount there is a loss of rs 2

Therefore the mark price of the pen can be calculated as follows

15% = c.p + 10 rs

25 % = c.p - 2 rs

25%-15% = 10 rs +2 rs

10% = 12 rs

10/100 = 12 rs

0.1= 12 rs

12/0.1

= 120 rs

Hence the mark price of the pen is 120 rs