A woman bought 130 kg of tomatoes for 52,000.00. She sold half of the tomatoes at a profit of 30%. The rest of the tomatoes began to go bad, she then reduced the selling price per kg by 12%. Calculate:
(a) the new selling price per kg;
(ii) the percentage profit on the entire sales if she threw away 5 kg of bad tomatoes.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a) Weight of full tomatoes = 130kg
Weight of half tomatoes = \(\frac{130}{2}\) = 65kg
Cost price of half tomatoes = \(\frac{N52,000}{2}\)
= N26,000
Profit = \(\frac{S.P - C.P}{C.P}\) x 100
30 = \(\frac{(S.P - 26,000)}{25,000}\) x 100
S.P = N7800 + N26,000
S.P = N7,800 + N26,000
S.P of half tomatoes = N33,800
Selling price per kg = \(\frac{33,800}{65}\)
= N520 per kg
Reduction in selling price = 12%
= \(\frac{12}{100}\) x 520 = N62.40k per kg
New selling price per kg
= N520 - N62.40k
= N457.60k
(b) 5kg is thrown away remaining 60kg
The selling price of entire 60kg
= 60 x N457.60k = N27,456
The entire selling price
N33,800 + N27,456
= N61,256
% profit = \(\frac{(61.256 - 50,000)}{52,000}\) x 100
= 17.8%
Source: Myschool Past Questions Archive (Record #58164)