the profit obtained when 135 chairs are sold is equal to the cost price of 60 chairs. what is the percentage profit obtained when 26 chairs are given free with the sale of 143 chairs?
Answers
Given :- The profit obtained when 135 chairs are sold is equal to the cost price of 60 chairs.
To Find :- what is the percentage profit obtained when 26 chairs are given free with the sale of 143 chairs ?
Solution :-
→ Profit = SP - CP
→ Profit = SP of 135 Chairs - CP of 135 chairs
{ Given that, Profit is Equal to CP of 60 chairs .}
So,
→ 60 chairs CP = SP of 135 Chairs - CP of 135 chairs
→ 60 chairs CP + 135 chairs CP = 135 chairs SP
→ 195 chairs CP = 135 chairs SP
→ CP / SP = (135/195)
→ CP / SP = (9/13)
→ SP / CP = (13/9)
→ SP = (13/9)CP --------- Eqn.(1)
now, given that,
→ 26 chairs = Given free with the sale of 143 chairs .
we can say that, when someone buy 143 chairs he gets 26 chairs free .
So,
→ Total chairs he gets = 143 + 26 = 169 chairs = 169CP .
Then,
→ SP of 143 chair = 143SP
putting value of Eqn.(1) ,
→ SP of 143 chair = 143 * {(13/9)CP} = (1859/9)CP .
Therefore,
→ Profit Earned = SP - CP = (1859/9)CP - 169CP = (1859 - 169*9)CP / 9 = (1859 - 1521)CP/9 = (338/9)CP .
Hence,
→ Profit % = (Profit * 100) / (Total CP of all chairs he gets.)
→ Profit % = [(338/9)CP * 100) / (169CP)
→ Profit % = (338 * 100) / (169*9)
→ Profit % = 22.22% (Ans.)
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Given : The profit obtained when 135 chairs are sold is equal to the cost price of 60 chairs.
To Find : profit percentage obtained when 26 chairs are given free with the sale of 143 chairs?
Solution:
Let say cost price of a chair = C
Selling price of chair = S
Cost price of 135 chairs = 135C
Selling price of 135 chairs =135S
Profit = 135S - 135C
Profit is equal to the cost price of 60 chairs. = 60C
Equating
135S - 135C = 60C
=> 135S = 195C
=> 9S = 13C
=> S = 13C/9
26 chairs are given free with the sale of 143 chairs
=> Total chairs given = 143 + 26 = 169
Cost Price = 169C
Selling Price = 143S = 143 (13C/9) = 1859C/9
Profit = 1859C/9 - 169C
= 338C/9
Profit % = 100 * ( 338C/9 )/169C
= 200/9
= 22.22 %
profit percentage obtained when 26 chairs are given free with the sale of 143 chairs = 22.22 %
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