a shopkeeper bought 80 apples of rs.50 each he sold some apples at 50%profit and some quantity of apples at 20% profit .if shopkeeper earned rs.1260 on total sold quantity and rs.560 on overall quantity , then find the quantity of apples sold by shopkeeper at 20% profit
Answers
Answer:
26 Apples sole at 20% Profit
Step-by-step explanation:
a shopkeeper bought 80 apples of rs.50 each
Total Cost = 80*50 = Rs 4000
Profit rs.560 on overall quantity
=> Sell Price = 4000 + 560 = Rs 4560
earned rs.1260 on total sold quantity
=> Cost Price of Sold Quantity = 4560 - 1260 = Rs 3300
Number Of Apples sold = 3300/50 = 66
Let say sold at 20% profit = X
Cost Price = 50X Rs
Sell Price = 50X + (20/100)50X = 60X Rs
then sold at 50% Profit = 66 - X
Cost Price = 50(66-X) = 3300 - 50X Rs
Sell Price = (3300 - 50X) + (50/100)(3300 - 50X)
= (3300 - 50X)(1.5)
= 4950 - 75X
Total Sell Price =
60X + 4950 - 75X = 4560
=> 15X = 390
=> X = 26
26 Apples sole at 20% Profit
Answer:
26 apples Sold @ 60 Rs.
Step-by-step explanation:
Cost Price: 50 Rs. per apple
50% Profit means apples were sold at: 50+ [50%/100]* (50)= 50+25= 75 Rs.
So he/she earns a profit of 25 Rs. on each apple sold at 75 Rs.
Similarly,
20% Profit means apples were sold at: 50+ [20/100]*50= 50+10=60 Rs.
Proft earned will be 10 Rs. on each apple sold at 60 Rs.
Now,
Let the shopkeeper sell X nos. of apples at the rate of 75 Rs.
and Y nos. of apples at the rate 60 Rs.
First Equation is:
[(profit earned of 75 Rs apple)*X]+[(profit earned on 60 Rs. apple)*Y]=1260Rs.
25*X + 10*Y=1260
Second Equation is:
actual apples were brought = 80 apples
purchase price= 50 Rs.
Total cost of purchase= 80*50= 4000 Rs.
Profit made by selling (X+Y) nos of apples= 560 Rs.
So, the shopkeeper has
4000+560 =4560 Rs. in his pocket now (by selling (X+Y) apples.
and X nos of apples were sold at 75 Rs. each and Y nos. of apples were sold at 60 Rs. each.
75*X + 60*Y = 4560
now solve for X and Y Linear equation
X= 40 Y= 26
thus 26 apples.