CAT 2024 Question Paper | Quant Slot 1

CAT Questions

CAT 2024 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 1 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

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Video Explanation

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Explanatory Answer

Ratio of number of apples and mangoes is \(5: 2\)
Let the Number of apples\(=5 x\)
Number of mangoes \(=2 x\)
Number of oranges \(=2 y\)
$$ 7 x+2 y=187--------(1) $$ She sells 75 apples, 26 mangoes and half of the oranges.
Number of unsold apples= \(5 x-75\)
Number of unsold mangoes \(=2 x-26\)
Number of unsold oranges \(=y\)
Ratio of unsold apples to unsold oranges=3:2
$$ \begin{array}{l} 5 x-75: y=3: 2 \\ 10 x-150=3 y \end{array} $$ $$ 10 x-3 y=150------(2) $$ Multiplying equation(1) with 3 , we get \(21 x+6 y=561\)
Multiplying equation(2) with 2 , we get \(20 x-6 y=300\)
Adding the above two equations, \(41 x =861\) $$ x=861 / 41=21 $$ Substituting \(x=21\) in equation 1 ,
$$ 7(21)+2 y=187 $$ $$ \begin{array}{l} 2 y=40 \\ y=20 \end{array} $$ Total number of unsold fruits \(=5 x-75+2 x-26+y=105-75+42-26+20=66\)

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The question 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 "

Hence, the answer is '66'

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