Question

Arunika bought some articles and sold half of them at ? 22,103 thereby making a profit of 15%. At what price should she sell the rest of them so as to earn an overall profit of 25%? A. RS. 25,947 B. RS. 24682 C. RS. 27130 D. RS. 23,528

Answer 1

let the C.P of the articles= 2x
S.P pf half articles =22103
profit=15%
therefore  using the formula
c.p=100/(100+ p%) * s.p
x=(100/115) * 22103
x=19220
therefore total c.p =2x
cp=38440
total profit =25%
total s.p= (100+p%)/100 * c.p
            = (125/100)*38440
             =48050
therfore s.p of other half of the articles
=48050-22103
=25947
so A) Rs 25947 is the answer

Answer 2

Solution :-

Let the cost price of all the articles be Rs. 'x' 
So, Cost price of half of the articles will be Rs. x/2

We know that S.P. = C.P. + Profit
Now, according to the question.
As it is given in the question that half of the articles were sold at 15 % profit.
So,
⇒ 22103 = x/2 + [(x/2)*15]/100
⇒ 22103 = x/2 + 15x/200
⇒ 22103 = x/2 + 3x/40
⇒ (20x + 3x)/40 = 22103
⇒ 23x/40 = 22103
⇒ 23x = 22103*40
⇒ x = 884120/23
⇒ x = 38440

So, Cost Price of all the articles is Rs. 38440.

Cost price of half of the articles = 38440/2 = Rs. 19220
Overall profit required to be earned = 25 %
So, 
Total profit @ 25 % = (38440*25)/100
Total profit to be earned @ 25 % = Rs. 9610

Profit already earned @ 15 % = S.P. of  half of the articles - C. P. of half of the articles 
⇒ 22103 - 19220
= Rs. 2883

Now, remaining profit to be earned = Rs. 9610 - 2883 
= Rs. 6727

So, Profit of Rs. 6727 is yet to be earned.

Selling Price of the remaining half of the articles = C.P. of remaining half of the articles + Remaining profit to be earned
⇒ 19220 + 6727
= Rs. 25947

S.P. of remaining half of the articles should be Rs. 25947, so that Arunika will be able to earn overall profit of 25 %.

So, the Option (A) is correct.