Aptitude - Profit and Loss - Discussion
Discussion Forum : Profit and Loss - General Questions (Q.No. 2)
2.
The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:
Answer: Option
Explanation:
Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x.
S.P. of x articles = Rs. 20.
Profit = Rs. (20 - x).
 |
 |
20 - x | x 100 = 25 |  |
| x |
2000 - 100x = 25x
125x = 2000
x = 16.
Video Explanation: https://youtu.be/sidqvjUoZxY
Discussion:
353 comments Page 2 of 36.
SAIRAM said:
9 years ago
Friends it is easy.
20 articles are bought.
Then cost price = 20(A)...i.e A is price of each article so cp = 20A.
And given that X articles are sold at B price, then selling price of X articles are = XB.
And given 20A = XB.
Given 25% profit.
So profit% = profit/cp * 100.
Given total profit so, consider 20 articles.
25 = (20B - 20A)/20A * 100;
100A = 80B
So, A/B = 4/5.
4B = 5A.
Given, 20A = XB.
4 * 5A = XB,
4 * 4B = XB,
16B = XB,
X =16.
20 articles are bought.
Then cost price = 20(A)...i.e A is price of each article so cp = 20A.
And given that X articles are sold at B price, then selling price of X articles are = XB.
And given 20A = XB.
Given 25% profit.
So profit% = profit/cp * 100.
Given total profit so, consider 20 articles.
25 = (20B - 20A)/20A * 100;
100A = 80B
So, A/B = 4/5.
4B = 5A.
Given, 20A = XB.
4 * 5A = XB,
4 * 4B = XB,
16B = XB,
X =16.
Omare Oréna said:
3 years ago
Calculating gain w.r.t a single article:
Assume 20 articles cost a certain Price, say 'P'.
That means C.P of 1 article = P/20
X articles were sold at a Price equivalent to the cost of 20 articles, 'P'
Similarly, S.P of 1 article = P/X.
(S.P - C.P)/C.P = 25/100.
Calculate that & find that X = 16.
N.B: For gain, X must be < 20 because fewer items cover the initial cost (investment) so that the rest of the items make up the profit.
Assume 20 articles cost a certain Price, say 'P'.
That means C.P of 1 article = P/20
X articles were sold at a Price equivalent to the cost of 20 articles, 'P'
Similarly, S.P of 1 article = P/X.
(S.P - C.P)/C.P = 25/100.
Calculate that & find that X = 16.
N.B: For gain, X must be < 20 because fewer items cover the initial cost (investment) so that the rest of the items make up the profit.
Habib said:
1 decade ago
Its very very simple....
Given, CP(20 Articles)=SP(X articles)...............A
Assume, CP of 1 article is Re.1,
CP of X artilcles is rs.X..............B
CP(20 Articles)=rs.20..................C
So A becomes,
rs.20 = SP(X articles).................D
Now, Profit = SP(X articles) - CP(X articles)
= 20 - x (from B&D)
Hence find profit %, (20-x)/x * 100
Given, CP(20 Articles)=SP(X articles)...............A
Assume, CP of 1 article is Re.1,
CP of X artilcles is rs.X..............B
CP(20 Articles)=rs.20..................C
So A becomes,
rs.20 = SP(X articles).................D
Now, Profit = SP(X articles) - CP(X articles)
= 20 - x (from B&D)
Hence find profit %, (20-x)/x * 100
Vinuta said:
8 years ago
Take 20 * c.p = y = > c.p = y/20;
And x * s.p = y = >s.p = y/x;
w.k.t profit% = (100*profit)/c.p;
profit = ((profit%) * c.p)/100;
profit = (25 * c.p)/100;
also profit = s.p - c.p.
(25 * c.p)/100 = (y/x) - (y/20);
= (20 * c.p)/x-c.p;
Take c.p as common
(25 * c.p)/100 = c.p((20/x)-1)
c.p get cancelled
Now,
25/100 = (20/x)-1;
1/4 = (20/x)-1;
(1/4)+1 = 20/x;
5/4 = 20/x;
x = 20*4/5
x = 80/5;
x = 16.
And x * s.p = y = >s.p = y/x;
w.k.t profit% = (100*profit)/c.p;
profit = ((profit%) * c.p)/100;
profit = (25 * c.p)/100;
also profit = s.p - c.p.
(25 * c.p)/100 = (y/x) - (y/20);
= (20 * c.p)/x-c.p;
Take c.p as common
(25 * c.p)/100 = c.p((20/x)-1)
c.p get cancelled
Now,
25/100 = (20/x)-1;
1/4 = (20/x)-1;
(1/4)+1 = 20/x;
5/4 = 20/x;
x = 20*4/5
x = 80/5;
x = 16.
Abhinav Sharma said:
1 decade ago
Now, This is simplest way I could relate:
No. of articles = 20.
Let CP of 1 article = Re. 1.
CP of 20 articles = Rs. 20 ..... (Eq. 1).
SP of 1 article = 1.25x1 = Rs. 1.25 (Since profit is 25%).
SP of X articles = 1.25X .... (Eq. 2).
Now, the statement says the CP of 20 articles = SP of "X" articles with a profit of 25% i.e. Eq. 1 = Eq. 2.
20 = 1.25X.
X= 20/1.25 = 16.
Hope it clears !.
No. of articles = 20.
Let CP of 1 article = Re. 1.
CP of 20 articles = Rs. 20 ..... (Eq. 1).
SP of 1 article = 1.25x1 = Rs. 1.25 (Since profit is 25%).
SP of X articles = 1.25X .... (Eq. 2).
Now, the statement says the CP of 20 articles = SP of "X" articles with a profit of 25% i.e. Eq. 1 = Eq. 2.
20 = 1.25X.
X= 20/1.25 = 16.
Hope it clears !.
Snist said:
9 years ago
It should be noted that only x items are to be considered among 20 items during problem-solving.
So, sp of x items = 20 (since given sp of x = cp og 20 ||consider each item is of rs. 1).
And, cp of x items = x (since he bought the x for rs. X. Likewise 20 items for rs. 20).
Profit for selling x items = sp of x - cp of x = 20 - x.
Profit% = (profit/cp) * 100.
= {(20-x)/x} * 100.
So, sp of x items = 20 (since given sp of x = cp og 20 ||consider each item is of rs. 1).
And, cp of x items = x (since he bought the x for rs. X. Likewise 20 items for rs. 20).
Profit for selling x items = sp of x - cp of x = 20 - x.
Profit% = (profit/cp) * 100.
= {(20-x)/x} * 100.
Anonymous said:
7 years ago
Hi guys, let me try it in a simpler way.
Let C.P of an article be 'y'.
Hence C.P of 20 articles ==> 20y.
But given that 20y = S.P of x articles.
and C.P of x articles is y*x.
Now the profit percentage is:
((S.P of x articles - C.P of x articles)) / C.P of x articles) * 100.
(20y - xy)/(xy) * 100 = 25 (as given profit is 25%)
y cancels out, so we simplify to get x = 16.
Let C.P of an article be 'y'.
Hence C.P of 20 articles ==> 20y.
But given that 20y = S.P of x articles.
and C.P of x articles is y*x.
Now the profit percentage is:
((S.P of x articles - C.P of x articles)) / C.P of x articles) * 100.
(20y - xy)/(xy) * 100 = 25 (as given profit is 25%)
y cancels out, so we simplify to get x = 16.
UMESH said:
1 decade ago
The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:
===> LET CP BE Rs 100
CP OF 20 =2000
SP OF 20 =2000*1.25(PROFIT) = 2500
SP OF 01 =2500/20 =125
THERFORE ANSWER = 2000/125 =16
OR
CP *20 =SP *X
PUT SP=1.25CP
NOW, CP*20=1.25CP*X
CANCEL CP FROM BOTH
X = 20/1.25 =16
===> LET CP BE Rs 100
CP OF 20 =2000
SP OF 20 =2000*1.25(PROFIT) = 2500
SP OF 01 =2500/20 =125
THERFORE ANSWER = 2000/125 =16
OR
CP *20 =SP *X
PUT SP=1.25CP
NOW, CP*20=1.25CP*X
CANCEL CP FROM BOTH
X = 20/1.25 =16
Dhanu said:
3 years ago
Selling Price of X article is 20 and, we have to find C.P. of this X article.
It can be calculated by using the formula of C.P. which is given below;
C.P. = 100/(100+Gain%) * S.P.
So, let C.P. be X.. And by given data Gain % = 25, and S.P. of X article = 20 putting this values we get,
X(c.p) = 100/(100+25) * 20(s.p).
X= (100/125) * 20,
= 0.8 * 20,
= 16.
It can be calculated by using the formula of C.P. which is given below;
C.P. = 100/(100+Gain%) * S.P.
So, let C.P. be X.. And by given data Gain % = 25, and S.P. of X article = 20 putting this values we get,
X(c.p) = 100/(100+25) * 20(s.p).
X= (100/125) * 20,
= 0.8 * 20,
= 16.
(3)
Pavan divi said:
1 decade ago
Let cost price of an article be "a"
Let selling price of an article be "b"
Cost price of 20 articles is the same as the selling price of x articles. i.e;
20*a = x*b.
Profit = 25%.
((total articles * b) - (total articles * a))/(total articles * a) = 25 /100.
=> (20b-20a)/20a = 1/4.
=> b=5a/4.
Substitute b in 1st equation,
x=16.
Let selling price of an article be "b"
Cost price of 20 articles is the same as the selling price of x articles. i.e;
20*a = x*b.
Profit = 25%.
((total articles * b) - (total articles * a))/(total articles * a) = 25 /100.
=> (20b-20a)/20a = 1/4.
=> b=5a/4.
Substitute b in 1st equation,
x=16.
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