A fruit vendor brought a bag full of mangoes to the market. He kept some of the mangoes into the basket and put them for sale. He sold one-third of the mangoes in the basket to Mr. A and adds 18 more to it. He sold three-fourth of the remaining mangoes in the basket to Mr. B, and adds 12 more to it, after which he left with 25 mangoes in his basket. How many mangoes did the fruit vendor take in his basket in the beginning?

Question

Arun selected an integer \( x \) between 2 and 40, both inclusive. He noticed that the greatest common divisor of the selected integer \( x \) and any other integer between 2 and 40, both inclusive, is 1. How many different choices for such an \( x \) are possible?

Answer 1

The correct answer is option (D):

51

Let's solve this problem using reverse reasoning, working backwards from the end.

At the end, the vendor had 25 mangoes.

Before adding 12 mangoes to Mr. B's purchase, the vendor had 25 - 12 = 13 mangoes.

These 13 mangoes represent one-fourth (1 - 3/4 = 1/4) of the mangoes remaining after Mr. A's purchase. So, before selling to Mr. B, there were 13 * 4 = 52 mangoes.

Before adding 18 mangoes to Mr. A's purchase, the vendor had 52 - 18 = 34 mangoes.

These 34 mangoes represent two-thirds (1 - 1/3 = 2/3) of the mangoes the vendor had in the beginning. Let 'x' be the initial number of mangoes. Then (2/3) * x = 34. Solving for x: x = 34 * (3/2) = 51

Therefore, the fruit vendor took 51 mangoes in his basket in the beginning.

The Correct Option is D

Solution and Explanation

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