Home
Class 12
MATHS
{:("Column A","The saving from a person'...

`{:("Column A","The saving from a person's income; and his expenditure. The ratio of Marc's income to his boss's is 3: 4. Their respective expenditure ratio is 1 : 2","Column B"),("The saving from income of Marc",,"The saving from income of Marc's Boss"):}`

A

If column A is larger

B

If column B is larger

C

If the columns are equal

D

If there is not enough information to decide

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the savings of Marc and his boss based on the given ratios of their incomes and expenditures. ### Step-by-Step Solution: 1. **Define the Ratios**: - Let Marc's income be represented as \(3k_1\) and his boss's income as \(4k_1\) (where \(k_1\) is a constant). - The ratio of their incomes is given as \(3:4\). 2. **Define Expenditures**: - Let Marc's expenditure be represented as \(k_2\) and his boss's expenditure as \(2k_2\) (where \(k_2\) is another constant). - The ratio of their expenditures is given as \(1:2\). 3. **Calculate Savings**: - Marc's savings can be calculated as: \[ \text{Savings of Marc} = \text{Income of Marc} - \text{Expenditure of Marc} = 3k_1 - k_2 \] - The boss's savings can be calculated as: \[ \text{Savings of Boss} = \text{Income of Boss} - \text{Expenditure of Boss} = 4k_1 - 2k_2 \] 4. **Compare Savings**: - We need to compare Marc's savings and his boss's savings: \[ \text{Savings of Marc} = 3k_1 - k_2 \] \[ \text{Savings of Boss} = 4k_1 - 2k_2 \] - To compare these, we can set up the inequality: \[ 3k_1 - k_2 \quad \text{vs} \quad 4k_1 - 2k_2 \] 5. **Rearranging the Inequality**: - Rearranging the inequality gives: \[ 3k_1 - k_2 > 4k_1 - 2k_2 \] \[ -k_2 > k_1 \quad \text{or} \quad k_1 < k_2 \] - This indicates that if \(k_1 < k_2\), then Marc's savings are greater. Conversely, if \(k_1 > k_2\), then the boss's savings are greater. 6. **Conclusion**: - Since we have no specific values for \(k_1\) and \(k_2\), we cannot definitively conclude which savings are larger. Therefore, we cannot determine if Column A (Marc's savings) is larger, Column B (Boss's savings) is larger, or if they are equal. ### Final Answer: Since the values of \(k_1\) and \(k_2\) can vary, the correct answer is: **Option D: There is not enough information to decide.**
Promotional Banner

Similar Questions

Explore conceptually related problems

The monthly incomes of A and B are in the ratio 3 : 2 , and the monthly expenditures of the two are in the ratio 4 : 3","Column B"),("Saving of A",,"Saving of B"):}

The ratio of the income to the expenditure of a family is 7: 6. Find the saving if the income is Rs 1400.

The ratio of the income to the expenditure of a family is 7: 6. Find the saving if the income is Rs 1400.

The ratio of incomes of two persons is 9:7 and the ratio of their expenditures is 4:3 . If each of them manages to save Rs 2000 per month, find their monthly incomes.

The ratio of incomes of two persons is 9:7 and the ratio of their expenditures is 4:3. If each of them saves Rs 200 per month, find their monthly incomes.

The incomes of X and Y are in the ratio of 8:7 and their expenditures are in the ratio 19 : 16 . If each saves Rs 1250, find their incomes.

Margarette works in a factory and earns Rs 955 per month. She saves Rs 185 per month from her earnings. The ratio of her income to her expenditure is:

Mark and Brand , two employess on of Intel Corporation have a discussion have a discussion regarding their incomes and expenditures over a dinner. It was found that their incomes are in the ration 3:4 and their expenditure are in the ratio 2: 1 respectively . It was found that Mark saves tow- third of his income . What fraction of his incomes does Brad save ?

A labourer earns Rs 1200 a month and spends Rs 800. Find the ratio of his saving to income