Averages , Ratio and Proportion Question 6 - CAT 2024
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:
Step-by-Step Explanation
Let the initial number of apples be 5x and mangoes be 2x.
Initial Oranges = 187 − (5x + 2x) = 187 − 7x
- Track the unsold quantities:
- Unsold Apples = 5x − 75
- Unsold Mangoes = 2x − 26
- Unsold Oranges = (187 − 7x)/2
- Use the final unsold ratio constraint:
(5x − 75)/((187 − 7x)/2) = 3/2
⟹ 2(5x − 75)/(187 − 7x) = 3/2
4(5x − 75) = 3(187 − 7x)
20x − 300 = 561 − 21x
41x = 861 ⟹ x = 21
- Calculate the total unsold fruits:
- Unsold Apples = 5(21) − 75 = 30
- Unsold Mangoes = 2(21) − 26 = 16
- Unsold Oranges = (187 − 7(21))/2 = 20
Total Unsold Fruits = 30 + 16 + 20 = 66
Correct Answer: 66
💡 FundaMakers Tip:
Express all counts in terms of a single ratio multiplier (x) right away. This limits the number of variables you have to track. Setting up the algebraic cross-multiplication for the unsold components gives you x = 21 quickly, making the final summation straightforward.