Question

A profit of Rs. 438500 accrued from business to 4 partner on ratio 3/5:14:2/3:4/7. Determine
the amount of profit of each partner.​
​

Answer 1

ANSWER:

Given:

• Total Profit = Rs. 438500
• Profit share of 4 partners = 3/5:14:2/3:4/7

To Find:

• Profit of each partner

Solution:

$\text{Let the profit of each partner be,}\\\\:\longrightarrow \dfrac{3}{5}x, 14x, \dfrac{2}{3}x, \dfrac{4}{7}x.\\\\\text{We are given that,}\\\\:\longrightarrow Total\:Profit\:=\:Rs.438500\\\\\text{So,}\\\\:\implies\dfrac{3}{5}x+\dfrac{14}{1}x+\dfrac{2}{3}x+\dfrac{4}{7}x=Rs.438500\\\\\text{Taking LCM of 5, 1, 3 and 7 as 105.}\\\\:\implies\dfrac{3}{5}x+\dfrac{14}{1}x+\dfrac{2}{3}x+\dfrac{4}{7}x=Rs.438500$

$:\implies\dfrac{63}{105}x+\dfrac{1470}{105}x+\dfrac{70}{105}x+\dfrac{60}{105}x=Rs.438500\\\\:\implies\dfrac{63+1470+70+60}{105}x=Rs.438500\\\\:\implies\dfrac{1663}{105}x=Rs.438500\\\\:\implies x=438500\times\dfrac{105}{1663}\\\\:\implies x=\dfrac{438500\times105}{1663}\\\\\text{Profit Share of each partner:}$

$\hookrightarrow1)\:\dfrac{3}{5}x=\dfrac{3}{5\!\!\!/}\times\dfrac{438500\times105\!\!\!\!\!/^{\:21}}{1663}=\dfrac{27625500}{1663}=Rs. 16,611.85\\\\:\hookrightarrow2)\:14x=14\times\dfrac{438500\times105}{1663}=\dfrac{644595000}{1663}=Rs. 3,87,609.7\\\\:\hookrightarrow3)\:\dfrac{2}{3}x=\dfrac{2}{3\!\!\!/}\times\dfrac{438500\times105\!\!\!\!\!/^{\:35}}{1663}=\dfrac{30695000}{1663}=Rs. 18,457.61\\\\:\hookrightarrow4)\:\dfrac{4}{7}x=\dfrac{4}{7\!\!\!/}\times\dfrac{438500\times105\!\!\!\!\!/^{\:15}}{1663}=\dfrac{26310000}{1663}=Rs. 15,820.81$

$\text{\bf{Therefore, final profits' shares are:}}\\\\\bf{:\hookrightarrow1)\:Rs. 16,611.85}\\\\\bf{:\hookrightarrow2)\:Rs. 3,87,609.7}\\\\\bf{:\hookrightarrow3)\:Rs. 18,457.61}\\\\\bf{:\hookrightarrow4)\:Rs. 15,820.81}$