CAT 2024 Question Paper | Quant Slot 2

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 12 A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes make up 40% of his stock. That day, he sells half of the mangoes, 96 bananas and 40% of the apples. At the end of the day, he ends up selling 50% of the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is

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Video Explanation

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Explanatory Answer

Let the total number of fruits= 5x.
Therefore, the number of mangoes in the stock= (40/100)*5x= 2x.
Let the number of apples= 5y.
He sold x mangoes, 96 bananas and 2y apples which is equal to 50% of the total fruits.
x+ 96+ 2y= 2.5x
2x+192+4y= 5x
192+ 4y= 3x
The smallest value of y which will satisfy the equation is y= 3.
192+ 12= 204= 3x
x= 68
The smallest possible total number of fruits in the stock at the beginning of the day is 5x= 5*68= 340.

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The question is "A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes make up 40% of his stock. That day, he sells half of the mangoes, 96 bananas and 40% of the apples. At the end of the day, he ends up selling 50% of the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is"

Hence, the answer is '340'

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