An article is sold at 20% profit. It its cost price is increased by Re 50 and at the same time if its selling price is also increases by Re 30. the percentage of profit decrease by ¹⁰/₃%. find the cost price.

As there is a increase in both cp and sp simultaneously, we cannot do this by ratio or short cut method.... Best time saving method is..... Go by options......
Cp-850 p%-20 .... Therefore sp-1020
Now, cp becomes 900 and sp becomes 1050....which provides u a profit% of 10/3%........

This is the optimum method...

Answer wil be 850 not 3000

=20-10/3
=1/6
= how could possible

let original
c.p=x, @20% profit
s.p=1.2x
now new
c.p=x+50
s.p=1.2x+30
ATQ
(1.2x+30-x-50)/x+50=(20-10/3)%
(.2x-20)/x+50=1/6
1.2x-120=x+50
.2x=170
x=850

Please show answer

CP is Increased by 50
SP is Increased by 30
So,
10/3 % ------------ 20
1% ----------------- 6
100% ------------- 600

Is the Answer

Rs 850

3000

3000

Let us Assume that The cost price of an article is "X";
Then Selling price of that article is X*120/100= 6X/5;
Profit= Selling price - Cost price; i.e., 6X/5-X= X/5;--------->(1)
Now the Same article cost price is increased by Rs. 50 i.e., X+50;
and the selling price is also Increased by rs. 30 i.e., 6X/5+30;= (6X+150)/5;
Now the profit is (6X+150)/5-(X+50);= (x-100)/5------->(2)
now the profit percentage decreases by 10/3% means ((1)-(2))*100/(1);=
(x/5-(X-100)/5)*100/(X/5)= 10/3; from this X= 3000; i.e., Cost price is 3000 rupees You may Cross check it out with this Cost price and u will also get the same Profit difference...

i think i follow the conventional method to solve this question. if any body can do it in a short cut method please let post here.