A man sold an article at k percent profit after offering k percent dis

Question

A man sold an article at k percent profit after offering k percent discount on the listed price. Had he sold the article at (k+15) percent discount on the listed price, his profit would have been (k-20) percent. What would have been his percent profit had he sold the article without offering any discount?

A. 5%
B. 10%
C. 25%
D. 33%
E. 38%

A. 5%
B. 10%
C. 25%
D. 33%
E. 38%

KarishmaB · Accepted Answer

The question talks about margin, discount and profit so we use:

(1 + \frac{m}{100})*(1 - \frac{d}{100}) = (1 + \frac{p}{100}) 
Margin Multiplier * Discount Multiplier = Profit Multiplier

We need the profit when discount is 0, so basically, we need the margin% i.e. by what %age has the cost price been bumped up. If no discount is given, that will be the profit%.

M * (1 - \frac{k}{100}) = (1 + \frac{k}{100})  ... (I)

M*(1 - \frac{(k + 15)}{100}) = (1 + \frac{(k - 20)}{100})

M*(1 - \frac{(k + 15)}{100}) = (1 + \frac{k}{100}) - \frac{20}{100}

Substituting from (I) on the right hand side, we get

M*(1 - \frac{k}{100}) - M*\frac{15}{100} = M*(1 - \frac{k}{100}) - \frac{1}{5}

-M*\frac{3}{20} = - \frac{1}{5}

M = \frac{4}{3} = (1 + \frac{m}{100})

m = 33%

chetan2u · Answer

The LP(listed price) and the CP(cost price) are the same in each case. 
 Case I  : A man sold an article at k percent profit after offering k percent discount on the listed price.
So SP = (100+k)CP
BUT k percent discount on the listed price means SP = (100-k)LP
So (100+k)CP=(100-k)LP.... \frac{LP}{CP}=\frac{100+k}{100-k} 
 Case II  : Had he sold the article at (k+15) percent discount on the listed price, his profit would have been (k-20) percent.
 SP = (100+(k-20))CP=(80+k)CP
BUT k+15 percent discount on the listed price means SP = (100-(k+15)LP=(85-k)LP
So 115+k=(80-k)LP.... \frac{LP}{CP}=\frac{80+k}{85-k} ..

From the two case, we get .... \frac{80+k}{85-k}=\frac{100+k}{100-k}.......8000+20k-k^2=8500-15k-k^2..........35K=500....k=\frac{100}{7}

Substitute in any of the cases to get LP..
 \frac{LP}{CP}=(100+\frac{100}{7})/(\frac{100-100}{7})=\frac{800}{7}/\frac{600}{7}=\frac{800}{600}=\frac{4}{3} 
Thus  LP=\frac{4}{3}CP

CASE III  If there was no discount on LP, that is SP=LP
Profit % = \frac{SP-CP}{CP}*100 ={(4/3)CP-CP}/CP= \frac{1}{3}*100=33.33%

D

Jansaida · Answer

Multiplying factor of profit= (Multiplying factor of listed price)*(Multiplying factor of Discount)

Profit and discount= k%

Multiplying factor of profit= (1+(k/100))

Multiplying factor of discount= (1-(k/100))

Multiplying factor of Listed price= (100+k)/(100-k) ---------> Equation 1

In the Next Scenario (k+15) Discount will lead to (k-20) profit

Applying the same formula 
 
Multiplying factor of profit= (Multiplying factor of listed price)*(Multiplying factor of Discount)

(1+((k-20)/100))= (Multiplying factor of listed price)* (1-((k+15)/100))

(Multiplying factor of listed price)= (80+k)/(85-k) -------------> Equation 2

Equating both the equations

(100+k)/(100-k)=(80+k)/(85-k)

k=14.28

Substituing k value in equation 1,

(Multiplying factor of listed price)=( 100+14.28)/(100-14.28)

(Multiplying factor of listed price)=1.33317778

(Multiplying factor of listed price)=1+0.33317778

Since there is no discount in the final scenario

(Multiplying factor of listed price)=Multiplying factor of profit

IMO the answer is 33.31 %.

warrior1991 · Answer

VeritasKarishma   chetan2u

Don't know how to solve??

Where to start ?? Please help

Harsh2111s · Answer

I got the correct answer.
But it took 5 min to solve those equations.
Is there any other way to solve this question?

srik410 · Answer

Profit percent = S/C-1 where S -> Final selling price after discount and C is the fixed cost
In delta form, Change in profit percent = (Change in S)/C because C is the same

From statement 1 and 2 we can say profit percent reduced by 20% when 15% discount is introduced on S or S/C
So, 20/100=15/100*S/C => S/C=20/15

They are asking what is the profit percent without any discounts ie S/C-1 = 20/15-1 or 33.33%

K812 · Answer

A quicker way to solve this question could be, by understanding the logic.

When we increase the discount by 15%, the profit reduces by 20%

So, when CP= x and LP = 100 and discount is k%, SP = 100-k- (1)
when discount is k+15%, SP= 85-k (2)

If we subtract the profit in case 1 from case 2, we get a 20% profit

So, 20% = (100-k-x)/x - (85-k-x)/x

Solving this we get x = 75

So, when there is no discount on LP, profit is 25/75 * 100

A man sold an article at k percent profit after offering k percent dis

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A man sold an article at k percent profit after offering k percent dis

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