CAT 2023 Quant was dominated by Arithmetic followed by Algebra. 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 14 : 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

Try upto 40 hours for free

Learn from the best!

Limited Seats Available - Register Now!

Since the mangoes make up 40% of his stock at the beginning of the day, and let the mangoes at the beginning of the day be 4x, So the bananas and apples will be equal to 6x. If the bananas equal y, then the apples would be 6x - y. Totally there are 10x number of fruits.

At the end of the day 50% of mangoes, 96 bananas and 40% of apples are sold and thereby he ends up selling 50% of the fruits.

\( 50 \% ( 4 x ) + 96 + 40 \% ( 6 x - y ) = 50 \% ( 10 x ) \)

\( 2 x + 96 + 2.4 x - 0.4 y = 5 x \)

\( 4.4 x + 96 - 0.4 y = 5 x \)

\( 96 - 0.4 y = 0.6 x \)

\( 480 - 2 y = 3 x \)

\( 3 x + 2 y = 480 \)

\( x = \frac { 480 } { 3 } - \frac { 2 } { 3 } y = 160 - \frac { 2 } { 3 } y \) (For x to be an integer, y should be a multiple of 3.)

Since y is the number of bananas, \( y \geq 96 \).

Also since the apples are (6x - y) in number...

(6x - y) = \( 6 \left( 160 - \frac { 2 } { 3 } y \right) - y \)= 960 - 5y

The number of apples must be non-zero.

960 - 5y = 0 when y = 192.

∴ 96 ≤ y < 192 (Also, y needs to be a multiple of 3.)

So, the maximum value that y can take is 189.

For the total number of fruits to be minimum, 10x should be minimum, which happens when x is minimum.

\( x = 160 - \frac { 2 } { 3 } y \); x is minimum when y is maximum.

So the minimum value of \( x = 160 - \frac { 2 } { 3 } \times 189 = 34 \)

So, the minimum number of total fruits = 10x = 340.

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 " **

Copyrights © All Rights Reserved by 2IIM.com - A Fermat Education Initiative.

Privacy Policy | Terms & Conditions

CAT^{®} (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.

2IIM Online CAT Coaching

A Fermat Education Initiative,

58/16, Indira Gandhi Street,

Kaveri Rangan Nagar, Saligramam, Chennai 600 093

**Mobile:** (91) 99626 48484 / 94459 38484

**WhatsApp:** WhatsApp Now

**Email: **info@2iim.com