Suhani pays tax at the rate of 30% on her entire income of Rs.90,000 and Ritika pays tax at the rate of 40% on her entire income of Rs.y. If the overall tax rate on their combined income comes to 37%, then what is the value of y?
Explanation:
To solve this problem, we need to find Ritika's income (Rs.y) such that the combined tax rate of Suhani and Ritika is 37%. Let's go through the calculations:
- Suhani's income: Rs.90,000
- Suhani's tax rate: 30%
- Ritika's tax rate: 40%
- Total income combined tax rate: 37%
First, calculate Suhani's tax:
\[ \text{Tax paid by Suhani} = 30\% \times 90,000 = Rs.27,000 \]
Next, denote Ritika's income as y.
Her tax paid is:
\[ \text{Tax paid by Ritika} = 40\% \times y = 0.4y \]
Together, they have a combined income of:
\[ 90,000 + y \]
The total tax paid by both is:
\[ 27,000 + 0.4y \]
The combined tax rate can be calculated as:
\[ \frac{27,000 + 0.4y}{90,000 + y} = 37\% = 0.37 \]
Cross-multiply to solve for y:
\[ 27,000 + 0.4y = 0.37 \times (90,000 + y) \]
\[ 27,000 + 0.4y = 33,300 + 0.37y \]
Subtract 0.37y from both sides:
\[ 27,000 + 0.03y = 33,300 \]
Solve for y:
\[ 0.03y = 33,300 - 27,000 \]
\[ 0.03y = 6,300 \]
\[ y = \frac{6,300}{0.03} \]
\[ y = 2,10,000 \]
- Option 4: Rs.2,10,000 is indeed the correct value of y.
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