Sure, let's solve the problem step-by-step.
Given:
- Panchali receives 5 times the profit of Vaidahi.
- Seta receives [tex]\( \frac{3}{4} \)[/tex] of Vaidahi's profit.
- Total profit of the firm is 234,000.
Let's denote Vaidahi's profit by [tex]\( x \)[/tex].
1. Express profits in terms of [tex]\( x \)[/tex]:
- Panchali's profit = [tex]\( 5x \)[/tex]
- Seta's profit = [tex]\( \frac{3}{4}x \)[/tex]
2. Set up the total profit equation:
The total profit is the sum of the profits of Vaidahi, Panchali, and Seta:
[tex]\[
x + 5x + \frac{3}{4}x = 234,000
\][/tex]
3. Combine like terms:
Add the coefficients of [tex]\( x \)[/tex]:
[tex]\[
1x + 5x + \frac{3}{4}x = 234,000
\][/tex]
Convert [tex]\( \frac{3}{4} \)[/tex] to a decimal to simplify:
[tex]\[
1x + 5x + 0.75x = 234,000
\][/tex]
4. Sum the coefficients:
Combine the terms:
[tex]\[
6.75x = 234,000
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
Divide both sides by 6.75:
[tex]\[
x = \frac{234,000}{6.75} = 34,666.67
\][/tex]
Therefore, Vaidahi's profit is 34,666.67.
6. Calculate Seta's share:
Seta's share is [tex]\( \frac{3}{4} \)[/tex] of Vaidahi's profit:
[tex]\[
\text{Seta's share} = \frac{3}{4} \times 34,666.67 = 26,000
\][/tex]
Thus, Seta's share of the profit is 26,000.
