Question

Mr. Teremere and \(M r\). Meretere have 5 chocolates and 3 chocolates with them respectively. Meanwhile Mr. Khabbu Singh joined them and all 8 chocolates were distributed equally among all these three people. In turn Khabbu Singh gave Rs. 16 to \(\mathrm{Mr}\). Teremere and Mr. Meretere, since Khabbu Singh did not has any chocolate. What is the difference of amounts received by Teremere and Meretere? Given that the amount was shared in proportion of chocolates received by Khabbu Singh. (a) Rs. 8 (b) Rs. 12 (c) Rs. 14 (d) Rs. 15

Short answer

Answer: Rs. 8

Step-by-step solution

Determine the distribution of chocolates after the arrival of Khabbu Singh.

To do this, we need to add the total number of chocolates (5 from Mr. Teremere and 3 from Mr. Meretere) and divide by 3 people. Total chocolates = 5 + 3 = 8 Now, let's divide the 8 chocolates equally among the 3 people: 8 chocolates ÷ 3 people = 8/3 8 chocolates were divided equally, which means 2 chocolates were given to each person: Khabbu Singh = 2 chocolates Mr. Teremere = 2 chocolates Mr. Meretere = 2 chocolates

Calculate the original chocolates

Khabbu Singh paid each person based on the difference from their original number of chocolates: Mr. Teremere had 5 chocolates originally - 2 chocolates after distribution = 3 chocolates Mr. Meretere had 3 chocolates originally - 2 chocolates after distribution = 1 chocolate

Calculate the amount paid to each person based on their original chocolates.

Since Khabbu Singh gave a total of Rs. 16 to Mr. Teremere and Mr. Meretere, and the amount paid is proportional to the difference in their original chocolates, we can calculate the amount given to each person: Share of Mr. Teremere = 3 chocolate units / 4 chocolate units * Rs. 16 Share of Mr. Teremere = (3/4) * 16 = Rs. 12 Share of Mr. Meretere = 1 chocolate unit / 4 chocolate units * Rs. 16 Share of Mr. Meretere = (1/4) * 16 = Rs. 4

Calculate the difference between the amounts received by Mr. Teremere and Mr. Meretere.

To find the difference between the amounts received by Mr. Teremere and Mr. Meretere, we simply subtract the lower amount from the higher amount: Difference = Rs. 12 (Mr. Teremere) - Rs. 4 (Mr. Meretere) = Rs. 8 Therefore, the difference between the amounts received by Mr. Teremere and Mr. Meretere is Rs. 8, which is option (a).

Key concepts

Quantitative Aptitude

Quantitative aptitude is a measure of an individual's numerical ability and accuracy in mathematical calculations. The skills that are tested include various branches of mathematics such as arithmetic, algebra, geometry, and data interpretation. Proportion word problems, like the one involving Mr. Teremere, Mr. Meretere, and Mr. Khabbu Singh, delve into the arithmetic aspect of quantitative aptitude.

Understanding quantitative aptitude is essential for solving problems that require application of concepts such as ratios, proportions, and the division of amounts. When faced with such problems, one must identify the key quantities involved, understand the relationships between them, and apply appropriate mathematical operations to find the desired solution. The problem outlined above could appear in competitive exams and recruitment tests, assessing the candidates' proficiency in applying mathematical concepts to real-world situations.

Let's quickly revise the steps taken to solve the problem: We started by computing how the chocolates would be divided equally, then figured out the number of chocolates each person is left with by comparing it to what they started with. Finally, since Khabbu Singh had no chocolate initially, he compensated the others with money, which was split in proportion to the number of chocolates lost. Ultimately, calculating the difference in amounts received allowed us to find our answer, reinforcing the practical application of quantitative aptitude in daily scenarios.

Ratio and Proportion

The concept of ratio and proportion is fundamental to understanding relationships between quantities. A ratio represents a comparison between two or more similar quantities by division, while a proportion states that two ratios are equivalent.

When we look at our problem involving Mr. Teremere, Mr. Meretere, and Mr. Khabbu Singh, the distribution of chocolates sets up a scenario that can be analyzed using ratios. After Khabbu Singh joined, the chocolates were redistributed, creating a ratio of distributed chocolates per person. Despite each receiving an equal number after redistribution, the compensation from Mr. Singh was based on the proportions of their original amounts.

Understanding Proportion in Compensation

The amount Khabbu Singh gave to Mr. Teremere and Mr. Meretere was in direct proportion to the chocolates they lost, which is another ratio. So, we used these proportional ratios to divide the total money. This demonstrates the real-life application of ratios and proportions—solving such problems often involves setting up ratios and scaling them in proportion to find an equitable division or distribution.

Division of Amounts

Division of amounts is a straightforward concept that requires dividing a total quantity into specified parts. It often goes hand in hand with the concept of ratio and proportion when the division is not equal and needs to be made according to a certain ratio.

In the textbook example, the division of the total money Khabbu Singh offered was based on the proportionate loss of chocolates by Mr. Teremere and Mr. Meretere. The key was to understand that while the chocolates were distributed equally after Khabbu Singh joined, the compensation was not to be divided equally, but rather proportionately.

Strategic Division

The strategy here is to calculate the division based on 'units' lost or gained. Mr. Teremere ended up losing more chocolates than Mr. Meretere did initially, hence received a larger share of the compensation. Although it might seem complicated at first, the division of amounts according to a certain ratio is a common scenario in many practical applications like splitting bills, distributing resources, or sharing profits, making it an important concept to grasp for everyday practical problem-solving.