Math, asked by umulAlia, 6 hours ago

1. If an article sold at a gain of 5% instead of being sold at a loss of 5%. A man gets Rs.5 more. What is the cost price of the article? (a) Rs. 50 (b) Rs. 40 (C) Rs. 60 (d) Rs. 80?? ​

Answers

Answered by tennetiraj86
1

Answer:

Option a

Step-by-step explanation:

Given :-

If an article sold at a gain of 5% instead of being sold at a loss of 5%. A man gets Rs.5 more.

To find :-

What is the cost price of the article?

a) Rs. 50 (b) Rs. 40 (C) Rs. 60 (d) Rs. 80

Solution :-

Let the cost price of the article be Rs. X

Gain on it = 5%

We know that

Selling Price = [(100+g)×CP]/100

=> SP = (100+5)×X/100

=> SP = 105X/100

=> SP = 21X/20

Selling Price of the article = Rs. 21X/20

Now,

Loss on it = 5%

We know that

Selling Price = [(100-l)×CP]/100

=> SP = 95×X/100

=> SP = 95X/100

=> SP = 19X/20

Selling Price of the article = Rs. 19X/20

Given that

If an article sold at a gain of 5% instead of being sold at a loss of 5%. A man gets Rs.5 more.

=> SP on gain = SP on loss + Rs. 5

=> SP on gain - SP on loss = Rs. 5

=> (21X/20)-(19X/20) = 5

=> (21X-19X)/20 = 5

=> 2X/20 = 5

=> X/10 = 5

=> X = 5×10

=> X = 50

=> Cost Price = Rs. 50

Answer:-

The Cost Price of the article is Rs. 50

Check :-

CP = Rs. 50

Gain %= 5%

SP = (100+g)CP/100

=> SP = (100+5)×50/100

=> SP = 105×50/100

=> SP = 105/2

=> SP = Rs. 52.50

Now

Loss% = 5%

SP = (100-l)CP/100

=> SP = (100-5)×50/100

=> SP = 95×50/100

=> SP = 95/2

=> SP = Rs. 47.50

The difference between the two selling prices

= 52.50-47-50

= 5

He gets Rs. 5 more .

Verified the given relations in the given problem.

Used formulae:-

  • Selling Price = [(100+g)×CP]/100

  • Selling Price = [(100-l)×CP]/100

  • CP = Cost Price

  • g = gain

  • l = loss

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