120 friends ordered 3 types of shakes - Mango shake, Banana shake and Vanilla shake. 18 friends took all three shakes while 60 friends took at least two shakes. The price of each shake is 1000 per unit and they were billed a total of 1,70,000. Find out how many friends took one shake and how many friends did not take any shake?

1. A

   30,30

2. B

   35,25

3. C

   45,15

4. D

   32,28

Appeared in: Haryana CHO - 2022

Explanation

• The total number of shakes sold is calculated by dividing the total bill (1,70,000) by the price per shake (1,000), which equals 170 shakes.
• The number of friends who had exactly two shakes is found by subtracting the number of friends who had three shakes (18) from the number who had at least two shakes (60), resulting in 42 friends.
• An equation is set up for the total shakes: 170 = (1 * E1) + (2 * 42) + (3 * 18), where E1 is the number of friends who took one shake. Solving this gives E1 = 32.
• The number of friends who took no shakes is found by subtracting the sum of all friends who took shakes (32 + 42 + 18 = 92) from the total number of friends (120), which results in 28.

Why Other Options Were Wrong

• Option A: This option incorrectly assumes 30 friends took one shake and 30 took none. This would lead to a total of 30 + (242) + (318) = 168 shakes, not 170. The number of friends would also not sum to 120.
• Option B: This option incorrectly assumes 35 friends took one shake and 25 took none. This would lead to a total of 35 + (242) + (318) = 173 shakes, which contradicts the calculated total of 170 shakes.
• Option C: This option incorrectly assumes 45 friends took one shake and 15 took none. This would lead to a total of 45 + (242) + (318) = 183 shakes, which is inconsistent with the total bill.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Set Theory and Arithmetic Word Problem as background academic context rather than a clinical decision trigger.
• This question tests general intelligence, specifically logical reasoning and arithmetic skills, which are essential components of nursing entrance examinations.
• Problem-solving skills are crucial for nurses in clinical settings to make quick, accurate decisions based on available data, similar to how this problem requires breaking down information to find a solution.
• What if the total bill was 1,80,000? The total shakes would be 180. The equation would be 180 = x + 138, so x (friends with 1 shake) = 42. Then, friends with no shakes would be 120 - (42+42+18) = 18. The answer would change to 42, 18.

How to Approach the Question

• First, identify all the given numerical values: total friends, price per shake, total bill, friends who took three shakes, and friends who took at least two shakes.
• Use the total bill and price per shake to calculate the total number of shakes sold. This is a key piece of information.
• Break down the phrase 'at least two shakes' to find the number of people who had 'exactly two shakes'.
• Set up an algebraic equation to represent the total number of shakes sold, using a variable for the unknown quantity (friends who took one shake).
• Solve the equation to find the number of friends who took one shake.
• Finally, subtract the sum of all friends who purchased shakes from the total number of friends to find those who bought none.

Concept Tested & Keywords

• Concept Tested: Set Theory and Arithmetic Word Problem
• Stem keywords: 120 friends, 3 types of shakes, at least two shakes, total bill, price per shake
• Lead-in keywords: Find out

Question ID

QdUw3VoGa-wQ-UWx7yLfsx

Copy ID