Acycle is sold at a gain of 10%. Had it been sold for 50 more, the pain would have been 12%. Find its cost price.
Answers
Let x be the Cost Price of Cycle.
SP when cycle is sold at gain of 12% = x+ 12x/100 = 112x/100
SP when cycle is sold at gain of 10% = x+ 10x/100 = 110x/100
112x/100 – 110x/100 = 50
2x/100 = 50
x= (50 × 100)/2
= 2,500
So, the cost price of Cycle is 2,500..
Given :-
→ A cycle is sold at a gain of 10%
→ If the cycle is sold more than Rs. 50 then gain will be 12%.
To find :-
→ Cost Price of the cycle .
Solution :-
Let the Cost Price of the cycle be Rs. X
Gain on it = 10%
We know that
Selling Price = [(100+g)/100]×Cost Price
=> Selling Price = [(100+10)/100]×X
=> Selling Price = (110/100)×X
=> Selling Price = 110X/100
Therefore, Selling Price = Rs. 11X/10
Given that
If the cycle is sold for Rs. 50 more then the Selling Price will be (11X/10)+50
=> Selling Price = Rs.(11X+500)/10
Gain percentage will be on it = 12%
We know that
Cost Price = (100×Selling Price)/(100+g)
=> X = [100×{(11X+500)/10}]/(100+12)
=> X = [10(11X+500)]/(112)
=> 112X = 10(11X+500)
=> 112X = 110X+5000
=> 112X-110X = 5000
=> 2X = 5000
=> X = 5000/2
=> X = 2500
Therefore, Cost Price = Rs. 2500
Answer :-
→ The Cost Price of the cycle is Rs. 2500
Check :-
The Cost Price of the cycle = Rs. 2500
Gain on it = 10%
Selling Price = [100+10)/100]×2500
=> Selling Price = (110/100)×2500
=> Selling Price = 110×25
Therefore, Selling Price = Rs. 2750
If Rs. 50 is increased in the selling price then it will be 2750+50 = Rs. 2800
Gain = Selling Price - Cost Price
=> Gain = 2800-2500 = Rs. 300
Gain percentage = (Gain/Cost Price)×100
=> G% = (300/2500)×100
=> G% = 300/25
=> G% = 12
Therefore, Gain percentage is 12%
Verified the given relations in the given problem.
Used formulae:-
→ Gain = Selling Price - Cost Price
→ Gain% = (Gain / Cost Price)×1000
→ Selling Price = [(100+g)/100]×Cost Price
Points to Know :-
→ Gain or Profit percentage is calculated on Cost Price.
→ Loss = Cost Price - Selling Price
→ Cost Price = (100×Selling Price )/100