The marked price of a chair and a table are in the ratio 2 : 3 respectively. The shopkeeper gives a 20% discount on the chair. If the combined discount on both the chair and the table is 26%, then what will be the discount given on the table?

Given:

Marked price of a chair and a table are in the ratio 2 : 3.

Formula used:

Selling price = Marked Price(100 - Discount)/100

Calculation:

Let the discount percentage on table be x.

Ratio of the marked price of a chair and a table = 2 : 3

Marked price of the Chair = Rs 200x

Marked price of the Table = Rs 300x

⇒ Combined price = Rs (200x + 300x) = Rs 500x

Discount = 26%

⇒ Combined selling price = Rs 500x (1 – 26/100) = Rs 370

In 1^st case,

⇒ Selling price of chair = Rs 200x (1 – 20/100) = Rs 160

In 2^nd case,

⇒ Selling price of table = Rs 300x (1 – x/100) = Rs (300 – 3x)

According to Question,

⇒ Combined selling price = Selling price of chair + Selling price of table

⇒ 370 = 160 + (300 – 3x)

⇒ x = 30%

∴ The discount given on the table is 30%.

Shortcut Trick The marked price of a chair and a table are in the ratio 2 : 3

Chair : Table

200 : 300

Total discount = 500 ×\(26\over100\) = 130

Discount on the chair = 200 × \(20\over100\) = 40

Discount on the table = 130 - 40 = 90

Percentage discount on the table = \(90\over300\) × 100 = 30%

∴ The percentage discount on the table is 30%.