NinetynineCAT 2024 Slot 1 QA Q1 Ratio, Mixtures & Averages
Question 1 of the Quantitative Ability (QA) section, CAT 2024 Slot 1, with CAT's official answer and a worked solution.
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
TITA: type in the answer. There are no options and no negative marking.
Answer: 66 Ratio, Mixtures & Averages TITA
Solution
- Let apples = \(5k\), mangoes = \(2k\), oranges = \(o\). Then \(7k + o = 187\).
- After the sales, unsold apples = \(5k - 75\) and unsold oranges = \(\frac{o}{2}\). Given \((5k-75) : \frac{o}{2} = 3 : 2\), so \(2(5k - 75) = \frac{3o}{2}\), i.e. \(o = \frac{20k - 300}{3}\).
- Substitute: \(7k + \frac{20k-300}{3} = 187 \Rightarrow 21k + 20k - 300 = 561 \Rightarrow k = 21\).
- So apples = 105, mangoes = 42, oranges = 40.
- Unsold: apples \(105 - 75 = 30\), mangoes \(42 - 26 = 16\), oranges \(20\). Total \(= 30 + 16 + 20 = 66\).
Shortcut. Apples must exceed 75, so \(k \ge 16\); and \(187 - 7k\) (oranges) must be even. Trying \(k = 21\) gives 40 oranges and the 3 : 2 ratio checks out immediately.