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Find the selling price of goods if two salesmen claim to make 25% profit each, one calculating it on cost price while another on the selling price, the difference in the profits earned being 100 rupees and selling price being the same in both the cases.

a) 2000 rupees

b) 1600 rupees

c) 2400 rupees

d) 2500 rupees
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Let cp = y and

sp = x.............(1)

case 1 (profit on cp): profit = sp - cp
0.25y = x - y
sp = x = 1.25y........(2)
profit = sp - cp = 1.25y - y = y/4

As we know selling price being the same in both the cases so from (1) and (2).

x = 1.25y  $\Rightarrow$ y= 0.8 x.........(3)

case 2 (profit on sp): profit = sp - cp
cp = sp - profit
x - 0.25x = y
cp = y = 0.75 x
profit= sp - cp = x - 0.75x = x/4

now x/4 - y/4 = 100(as given in the question)
put value of y from (3)
0.25x - 0.8x/4 =100

0.25 x - 0.2 x = 100

x = 2000

Hence the selling price of goods if two salesmen claim to make 25% profit each is Rs 2000.

Hence Option A is the Correct Answer..

by Loyal (5.5k points)
edited
0

@Shubham Sharma 2 but the answer is a) 2000 which is selling price( in the question it is mentioned that they are asking about selling price)

putting in case 1, sp = 1500

putting in case 2, sp = 1600.

But not 2000.??

0

edited @Shubhanshu

Given, 2 seller selling the good
Seller 1 claim he made 25% profit on Cost price.
Seller 2 claim he made 25% profit on selling price.

Lets selling price be y                    --------------------- 1

Lets take seller 2 first
He's claims that he made 25% profit on selling price.
i.e his cost price would be y - $\frac{25y}{100}$ = $\frac{75y}{100}$
Profit he made = selling price - cost price = y - $\frac{75y}{100}$ = $\frac{25y}{100}$     ---------------------- 2

Now lets take seller 1 next
He is claiming he made 25% profit on cost price, lets his cost price be x
so his selling price will become = x + $\frac{25x}{100}$ = $\frac{125x}{100}$         ----------------------- 3
Profit he made = selling price - cost price = $\frac{125x}{100}$ - x = $\frac{25x}{100}$  ----------------------- 4

From 1 and 3
Since its given selling price is same so y = $\frac{125x}{100}$ i.e x = $\frac{100y}{125}$ -------------------- 5

From 2 and 4
Its given in question there is a difference of 100 rs between profit made by both the seller so we can write
$\frac{25y}{100}$  - $\frac{25x}{100}$ = 100
25y - 25x = 10000
25y - $\left ( 25 \times \frac{100y}{125} \right )$ = 10000 (from 5)
5y = 10000
y = 2000
i.e selling price is 2000 rs
option a is correct here.

by Loyal (7.7k points)
edited by