An item, when sold at a certain price, yields r% profit. Had it been s

Question

An item, when sold at a certain price, yields r% profit. Had it been sold for $s more, the profit percentage would have been t%. What is its cost price?

A. 100r/(t-s)
B. 100s/(t-r)
C. s/100(t-r)
D. st/100(t-r)
E. (t-r)/100s

DhruvS · Accepted Answer

Let "S" represents the Selling Price Let "C" represents the Cost Price Hence Initial profit (r%) = *100 --------eq.(1) Now they say if the Selling Price was $s more, the profit percentage would have been t% Now lets try to evaluate this as below: Hence New profit (t%) = *100 Now let's try to breakdown the above equation => (t%) = { *100} + {(s/C)*100} Now if we look closely at the above breakdown the first part i.e. { *100} is nothing but (r%) i.e. eq(1) Hence the final Equation comes down to (Note: I am dropping % sign for more clarity in below equation): => t = r + => (t - r) = (s/c) * 100 => c = 100s/(t - r) Which is nothing but Option (B) Kudos are appreciated if you liked my solution.

KarishmaB · Answer

Since we are dealing with many variables here, if you don't want to assume values, just note that an incoming of s extra dollars increases profit % from r% to t%. This extra percentage was achieved by $s.

s = (t - r)% of Cost Price

Cost Price = 100s/(t - r)

Answer (B)

warrior1991 · Answer

Let the profit be p . 
The CP be denoted by c

From the first case using Profit % formula.

r=(p*100)/c ---1

After S.P is increased by  s $

t=((p+ s )*100)/c----2

Therefore from 1 and 2

r/t=p/(p+s)

pr+sr=pt

p(t-r)=sr

Put value of r from e.q-1---

p(t-r)=s(p*100)/c

Both P got cancelled

(t-r)=100s/c

c=100s/(t-r)

IMO B.

warrior1991 · Answer

From the first case using Profit % formula.

r=(p*100)/c ---1

After S.P is increased by  s $

t=((p+ s )*100)/c----2

Therefore from 1 and 2

r/t=p/(p+s)

pr+sr=pt

p(t-r)=sr

Put value of r from e.q-1---

p(t-r)=s(p*100)/c

Both P got cancelled

(t-r)=100s/c

c=100s/(t-r)

IMO B.

Ish1996 · Answer

where did you get pr+sr=pt from? can you please explain this? Also is there any general topic that these equations are derived from?

warrior1991 · Answer

Read the equation just above the equation you talking about

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SchruteDwight · Answer

Above solutions are unnecessarily difficult

P=R-C

r(C)/100=R-C –> R=C(r/100+1)

t(C)/100=R+s-C –> t(C)/100=C(r/100+1)+s-C –> t(C)/100=r(C)/100+s –> C=S/((t-r)/100)=100(S)/(t-r)

nurulhoque · Answer

Essentially we are dealing with three numbers. Suppose we are starting with 20, after r% profit the number becomes 30 and adding 10 the number finally becomes 40. That is 20...30...40
Now r=50  
S= 10
t= 100  
If we substitute these values the correct expression must give the cost, which is 20.
A. 100r/(t-s) =100*50/90  
B. 100s/(t-r) =100*10/50 =20  
C. s/100(t-r) = 10/100*50  
D. st/100(t-r) =10*100/100*50  
E. (t-r)/100s = 50/100*10

Therefore, B is the answer.

Please note that I avoided using 100 as the starting value because often time it cannot eliminate all the incorrect answers. Hope this helps!

viveks55 · Answer

We can do this type of questions by assuming the numbers and checking them in answer options.
Let Cp = 100, Sp= 120
in that case r = 20%
When $s is added the profit will be t%.
Let $s be 30 in then t%(new profit) = 50%

Check the value in given answer option it should come as 100. Only option B satisfies as it gives CP as 100 where other options dosen't give. 
 Ans- Option B

viveks55 · Answer

We can do this type of questions by assuming the numbers and checking them in answer options.
Let Cp = 100, Sp= 120
in that case r = 20%
When $s is added the profit will be t%.
Let $s be 30 in then t%(new profit) = 50%

Check the value in given answer option it should come as 100. Only option B satisfies as it gives CP as 100 where other options dosen't give. 
 Ans- Option B 
 
You win trophies in your practices, you just pick them up in the games.

rrdeo22 · Answer

Here we can say that by adding $s to selling price, additional profit (other than r) will be the profit with respect to s i.e. s/c*100.

Thus,
t = r + 100s/c
t-r = 100s/c => c = 100s/(t-r)

bumpbot · Answer

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An item, when sold at a certain price, yields r% profit. Had it been s

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