Question

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

Answer:

Cost price of the sofa set is Rs 3200

Step-by-step explanation:

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