Aptitude - Profit and Loss - Discussion

I hope this helps you out guys.

S.P=18700(Given).
Loss%=15%(given).
We need to find out S.P so that the gain % becomes 15%.

Gain% must be = 15%(as per question).
so S.P = 115% OF C.P(Formula-derived).

C.P=(100/100-LOSS%)* S.P(Formula).

Note: we could have taken this formula also C.P=(100/100+GAIN%)*S.P, but for gain, S.P is NOT GIVEN so we don't use this one.

C.P=(100/100-15)*18700.
C.P=(100/85)*18700.
C.P=22000.

For gain of 15%.
S.P must be= 115% of C.P (mentioned above).
S.P=115/100*22000.
S.P=25300.(ANSWER).

We could solve this sum by using percentage method.

Let C. P = 100%
If person loss 15% of 100% so C. P = 85%.
85% = 18700 then;
100% = X,
85X = 18700* 100 = 1870000.
X = 1870000/85.
= 22000.

So now we find C. P = 22000.
Hence gain= C. P - S. P.
= 22000 - 18700
= 3300.

Therefore, by final condition.

Total gain to find = 100 + 15 =115,
So, by percentage method,
If 100= 22000,
115 = X.
So, 100x = 22000*115
X = 22000* 115/100.
X = 25300.

Here in first scenario:

SP:18,700 loss=15%
To find SP =? when gain=15%.

Solution:
Finding overall CP:

CP = 100/(100=15) * 18700
CP = 22000.

Gain % is given. So using the gain formula we can find the gain amount and from that, we can find SP.

To find gain:

15=(gain x 100)/2200
gain=3300.
therefore gain=SP-CP
we know gain and CP, we substitute in the above equation and find SP for 15% gain;
3300 = SP - 22000.
SP = 25,300.

Thank you.

Old (Loss)
Selling Price = 18700.
Loss = 15%.

Cost Price = (100/(100-15)) * 18700)// use Cost Price Formula.
= (100/85) * 18700.
= 22000 // Note : C.P remains same through out business

New ( Gain)

Cost Price = 22000// Retrieve C.P from above as C.P remains same no matter what,
Gain = 15 %.
Selling Price = ((100 + 15)/100) * 22000 // use S.P formula.
= (115/100) * 22000.
= Rs. 25300.

New selling price to gain 15% profit is Rs. 25300.

We can find out this solution in another way ..which is the easiest way.that is in this question he gave sp and loss is 15% so from these values we can calculate cp that is;
Sp = (100-15)% of cp.

So you can get cp is 22000.

So compare both cp and sp, we can get the loss is L = cp-sp = 22000 - 18700 = 3300.
So, in order to cover this loss of 15% simply add this loss value to the cp and then we can get 22000 + 3300 = 25300.

The formula used for this solution is:-

Selling price at a 15% loss is 18700, .i.e, for 100 rupees of investment we got only 85 rupees.

Same way to get a profit of 15% .i.e, for 100 rupees we have to get 115 rupees.

So, 85 rupees at 15% loss(100-15=85)=C.p 18700
So, 115 rupees at 15% gain (100+15=115)= C.p ?

85=18700
115=?

? = ( 18700*115 )/85 = 220*115 = 25300

S.p= 25300 with the gain of 15%.

S.P = 18700.

And loss = 15%.

So C.P = S.P/100-loss% (as S.P = (100-loss%)C.P).

Now C.P = 18700/0.85-----(1).

At what price must that plot be sold in order to gain 15%? (this is our second statement).

Let S.P=x.

So C.P = S.P/100+gain%.

Now our C.P = x/1.15------(2).

Now equate 1 and second C.P.

i.e x/1.15 = 18700/0.85.

After solving we will get x that is S.P for second statement = 25300.

Easy by knowing the formula.

s.p formula s.p=100-loss/100*c.p
so, 18700=85/100*c.p
1870000=85*c.p
1870000/85=c.p
22000=c.p

Then keep s.p ,as a x for gain 15% & gain=x-22000(s.p-c.p).
by formula gain % = 100 * gain/c.p.

So, 15=100/c.p*(x-22000)
15*220=x-22000
3300=x-22000
22000+3300=x.

ANS: 25300.

sp = cp*mf.

Here sp = 18700 and mf(multiplying factor) if loss is 15% = 1-0.15 = 0.85.

Hence cp = sp/mf.
cp = 18700/0.85 = 22000.

Again if he wants gain of 15% then sp will be sp = cp*mf.
mf here in case of gain will be 1+0.15 = 1.15.
hence sp will be = cp*1.15.
CP, as calculated, is 22000.
SP = 22000*1.15 = 25300.

Given s.p=18700,loss=15%;

then c.p=s.p+loss,

=>c.p=Rs.21505/-
....................................

gain=s.p-c.p;

gain%=(gain/c.p)*100;

15=(gain/21505)*100;

15=((s.p-21505)/21505)*100;

If he sells the plot for 25300(option c) the gain%=17.64.

to get gain% of 15% he should sell the plot for Rs.24730.75/-