A fruit seller has a total of 187 fruits consisting of apples, mangoes and oranges. The number of apples and mangoes are in the ratio 5 : 2. After she sells 75 apples, 26 mangoes and half of the oranges, the ratio of number of unsold apples to number of unsold oranges becomes 3 : 2. The total number of unsold fruits is
Question:
A fruit seller has a total of 187 fruits consisting of apples, mangoes and oranges. The number of apples and mangoes are in the ratio 5 : 2. After she sells 75 apples, 26 mangoes and half of the oranges, the ratio of number of unsold apples to number of unsold oranges becomes 3 : 2. The total number of unsold fruits is
A fruit seller has a total of 187 fruits consisting of apples, mangoes and oranges. The number of apples and mangoes are in the ratio 5 : 2. After she sells 75 apples, 26 mangoes and half of the oranges, the ratio of number of unsold apples to number of unsold oranges becomes 3 : 2. The total number of unsold fruits is
Options
Answer: 66
Explanation:
Let apples = A, mangoes = M, oranges = O. Given: A + M + O = 187 A : M = 5 : 2 ⇒ A = 5k, M = 2k for some k ⇒ 7k + O = 187 ⇒ O = 187 − 7k After selling: Unsold apples = A − 75 = 5k − 75 Unsold mangoes = M − 26 = 2k − 26 Unsold oranges = half remain = O/2 = (187 − 7k)/2 Given unsold apples : unsold oranges = 3 : 2, so (5k − 75) / ((187 − 7k)/2) = 3 / 2 Solve: 2(5k − 75) = 3(187 − 7k)/2 Multiply both sides by 2: 4(5k − 75) = 3(187 − 7k) 20k − 300 = 561 − 21k 41k = 861 k = 21 So: A = 5k = 105 M = 2k = 42 O = 187 − 7k = 40 Unsold: Apples = 105 − 75 = 30 Mangoes = 42 − 26 = 16 Oranges = 40 / 2 = 20 Total unsold fruits = 30 + 16 + 20 = 66 Answer: 66.
Explanation:
Let apples = A, mangoes = M, oranges = O. Given: A + M + O = 187 A : M = 5 : 2 ⇒ A = 5k, M = 2k for some k ⇒ 7k + O = 187 ⇒ O = 187 − 7k After selling: Unsold apples = A − 75 = 5k − 75 Unsold mangoes = M − 26 = 2k − 26 Unsold oranges = half remain = O/2 = (187 − 7k)/2 Given unsold apples : unsold oranges = 3 : 2, so (5k − 75) / ((187 − 7k)/2) = 3 / 2 Solve: 2(5k − 75) = 3(187 − 7k)/2 Multiply both sides by 2: 4(5k − 75) = 3(187 − 7k) 20k − 300 = 561 − 21k 41k = 861 k = 21 So: A = 5k = 105 M = 2k = 42 O = 187 − 7k = 40 Unsold: Apples = 105 − 75 = 30 Mangoes = 42 − 26 = 16 Oranges = 40 / 2 = 20 Total unsold fruits = 30 + 16 + 20 = 66 Answer: 66.
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