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
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