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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