Question

A shopkeeper sold a sofa set at 8% gain . Had he purchased it for 5% less and sold it for₹ 36 less than what he actually sold it for,he would have gained 12 and 1/2% . For how much did the man purchase the sofa set?

Answer 1

Let the cost price of the sofa set be Rs x
Given gain = 8% 
Therefore selling price of sofa set = [(100 +g)/100] x CP
= (108x/100)
Given when CP of sofa set is 5% less than the SP is Rs 36 less than actual selling price
Gain = 12.5%
CP of sofa set = CP(100 – l)/100
= x(100 – 5)100
= 95x/100
Hence the selling price of sofa set becomes,
(108x/100) – 36
Therefore gain = [(108x/100) – 36] – [95x/100]
= [13x/100] – 36
Gain% = [gain/CP] x 100
That is, 12.5 = [(13x/100) – 36]/[95x/100] × 100
On simplification, we get
x = 3200
 ∴ Cost price of the sofa set is Rs 3200