# A man sells an article at profit of 25%.If he had bought it at 20% less and sold it for 10.50 less, then he would have gained 30%. Find the cost price of the article

2
by sammysanmehta

• Brainly User
2014-09-16T09:56:20+05:30
Let original cost price = k. Then selling price at 25% profit = 1.25k.

If he had bought at 20% less of the cost price, i.e.,at 80% of cost price, then his cost price would have been = 0.8k.
Then selling price would be 10.50 less than original selling price 1.25k, his selling price would have been = 1.25k - 10.50.
Therefore his profit would have been = SP - CP = (1.25k - 10.5) - 0.8k
= 0.45k - 10.5.
This profit of (0.45k - 10.5) is on the cost price 0.8k.
Hence profit % = (Profit / CP) x 100
= [(0.45k - 10.5) / 0.8k] x 100 = 30
or 0.21k = 10.5 ==> k = 10.5 / 0.21 = 50
2014-09-16T12:01:02+05:30
Let the cp=x
sp at profit of 25%=125x/100=1.25x

if the cp had been 8x/10=0.8x and sp=1.25x-10.50
profit=30%
ATQ,
0.8x+0.3*0.8x=1.25x-10.50
⇒0.8x+0.24x=1.25x-10.50
⇒1.04x=1.25x-10.50
⇒10.50=0.21
⇒x=1050/21=50
So the cost price of the item is 50