Jai spends his income in the ratio of 5 : 3 : 2 in 2018 on investment, food and furniture respectively. Veer spend his income in the ratio of 1:2:4 in 2018 on food, furniture and investment respectively. Find the money spend on furniture by Jai and Veer together.
Show Hint
Always double-check which component of the ratio represents the target category.
For Jai: the 3rd term (2) represents furniture.
For Veer: the 2nd term (2) represents furniture.
Step 1: Understanding the Concept:
To find the amount spent on a specific category from a given ratio, we multiply the total income by the proportion corresponding to that category in the ratio. Key Formula or Approach:
If an amount \(I\) is divided in the ratio \(a : b : c\), the share of the second component is:
\[ \text{Share} = \frac{b}{a + b + c} \times I \] Step 2: Detailed Explanation:
Let us calculate the expenditure on furniture for each person in 2018:
1. For Jai (Jay) in 2018:
- Total Income = 60 thousand = \(\text{Rs. } 60000\)
- Ratio (Investment : Food : Furniture) = \(5 : 3 : 2\)
- Sum of ratio parts = \(5 + 3 + 2 = 10\text{ parts}\)
- Furniture share corresponds to 2 parts of this total:
\[ \text{Jai's Expenditure on Furniture} = \frac{2}{10} \times 60000 = \text{Rs. } 12000 \]
2. For Veer in 2018:
- Total Income = 70 thousand = \(\text{Rs. } 70000\)
- Ratio (Food : Furniture : Investment) = \(1 : 2 : 4\)
- Sum of ratio parts = \(1 + 2 + 4 = 7\text{ parts}\)
- Furniture share corresponds to 2 parts of this total:
\[ \text{Veer's Expenditure on Furniture} = \frac{2}{7} \times 70000 = \text{Rs. } 20000 \]
3. Calculate the combined expenditure on furniture:
\[ \text{Total Combined Expenditure} = 12000 + 20000 = \text{Rs. } 32000 \]
This matches Option B. Step 3: Final Answer:
The total combined money spent on furniture is Rs. 32000.
