Question

Vaidegi sold two sarees for ₹ 2200 each. On one she gains 10% and on the other she loses 12%. Find her total gain or loss percentage in the sale of the sarees

Answer 1

Saree 1 :

The selling price is ₹ 2200, let cost price be C.P₁, gain is 10%. We need to find C.P₁

Using the formula

S.P = `"C.P"_1(1 + ("gain"%)/10)` and substituting the values

2200 = `"C.P"_1(1 + 10/100)`

∴ C.P₁ = `2200 xx 100/110`

= 2000

Saree 2 :

The selling price is 2200, let cost price be CP₂, loss is given as 12%. We need to find CP₂ 

using the formula as before,

S.P = `"C.P"_2 (1 - ("loss"%)/100)` and substituting the values

2200 = `"C.P"_2 (1 - 12/100)`

= `"C.P"_2 xx ((100 - 12)/100)`

= `"C.P"_2 xx 88/100`

∴ C.P₂ = `(2200 xx 100)/88`

= 2500

∴ Cost price of both together is C.P₁ + C.P₂ 

= 2000 + 2500 = 4500 ...(1)

Selling price of both together is 2 × 2200 = 4400 ...(2)

Since net selling price is less than net cost price, there is a loss.

Loss % = `"loss"/"cost price" xx 100`

Loss = Net cost price – Net selling price

(1) – (2) = 4500 – 4400 = 100

∴ loss % = `100/4500 xx 100`

= `100/45`

= `20/9`

= `2 2/9%`

= `2 2/9%` loss