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

$\bf \underline{Given} :$ ↴

$\sf \implies Total \: profit = Rs. \: 438500$

$\sf \implies Profit \: share \: of \: 4 \: partners = \dfrac{3}{5} : 14 : \dfrac{2}{3} : \dfrac{4}{7}$

$\bf \underline{To \: find} :$ ↴

$\sf \implies Profit \: share \: of \: each \: partner.$

$\bf \underline{\underline{Solution}}$

$\sf Let \: the \: profit \: of \: each \: partner \: be \: \dfrac{3}{5}x,\:14x,\:\dfrac{2}{3}x,\:\dfrac{4}{7}x$

$\sf Here, the \: total \: profit \: is \: Rs. \: 438500$

$\sf \implies \dfrac{3}{5}x+ \dfrac{14}{1} x+\dfrac{2}{3}x+\dfrac{4}{7}x \: = Rs. \: 438500$

$\sf \underline{Making \: the \: denominators \: as \: same}.$

$\sf LCM \: of \: \underline{ 5, \: 1, \: 3, \: 7 } \: is \: 105$

$\sf \implies \dfrac{3}{5} \times \dfrac{21}{21} = \dfrac{63}{105} x$

$\sf \implies \dfrac{14}{1} \times \dfrac{105}{105} = \dfrac{1470}{105} x$

$\sf \implies \dfrac{2}{3} \times \dfrac{35}{35} = \dfrac{70}{105} x$

$\sf \implies \dfrac{4}{7} \times \dfrac{15}{15} = \dfrac{60}{105} x$

$\bf \underline{ Now},$

$\sf\implies\dfrac{63}{105}x+\dfrac{1470}{105}x+\dfrac{70}{105}x+\dfrac{60}{105}x=Rs. \: 438500$

$\sf \underline{Taking \: denominators \: as \: common}.$

$\sf\implies\dfrac{63 + 1470 + 70 + 60}{105} \: x \: = Rs. \: 438500$

$\sf\implies\dfrac{1663}{105} \: x \: = Rs. \: 438500$

$\sf\implies x = 438500 \times \dfrac{105}{1663}$

$\sf \underline{Simplifying \: the \: above \: expression}.$

$\sf\implies x = \dfrac{46042500}{1663}$

$\sf \underline{Now, profit \: share \: of \: each \: partner \: is} :$

$\sf\implies 1^{st} \: patner \: = \dfrac{3}{5}x = \dfrac{3}{5} \times \dfrac{46042500}{1663} \: = Rs. \: 16611.85$

$\sf\implies 2^{nd} \: patner \: = 14x=14\times\dfrac{46042500}{1663}=Rs. \: 3,87,609.7$

$\sf\implies 3^{rd} \: patner \: = \dfrac{2}{3}x = \dfrac{2}{3} \times \dfrac{46042500}{1663} \: = Rs. \: 18457.61$

$\sf\implies 4^{th} \: patner \: = \dfrac{4}{7}x = \dfrac{4}{7} \times \dfrac{46042500}{1663} \: = Rs. \: 15820.81$

Answer 2

Explanation:

$\bf \underline{Given} :$ ↴

$\sf \implies Total \: profit = Rs. \: 438500$

$\sf \implies Profit \: share \: of \: 4 \: partners = \dfrac{3}{5} : 14 : \dfrac{2}{3} : \dfrac{4}{7}$

$\bf \underline{To \: find} :$ ↴

$\sf \implies Profit \: share \: of \: each \: partner.$

$\bf \underline{\underline{Solution}}$

$\sf Let \: the \: profit \: of \: each \: partner \: be \: \dfrac{3}{5}x,\:14x,\:\dfrac{2}{3}x,\:\dfrac{4}{7}x$

$\sf Here, the \: total \: profit \: is \: Rs. \: 438500$

$\sf \implies \dfrac{3}{5}x+ \dfrac{14}{1} x+\dfrac{2}{3}x+\dfrac{4}{7}x \: = Rs. \: 438500$

$\sf \underline{Making \: the \: denominators \: as \: same}.$

$\sf LCM \: of \: \underline{ 5, \: 1, \: 3, \: 7 } \: is \: 105$

$\sf \implies \dfrac{3}{5} \times \dfrac{21}{21} = \dfrac{63}{105} x$

$\sf \implies \dfrac{14}{1} \times \dfrac{105}{105} = \dfrac{1470}{105} x$

$\sf \implies \dfrac{2}{3} \times \dfrac{35}{35} = \dfrac{70}{105} x$

$\sf \implies \dfrac{4}{7} \times \dfrac{15}{15} = \dfrac{60}{105} x$

$\bf \underline{ Now},$

$\sf\implies\dfrac{63}{105}x+\dfrac{1470}{105}x+\dfrac{70}{105}x+\dfrac{60}{105}x=Rs. \: 438500$

$\sf \underline{Taking \: denominators \: as \: common}.$

$\sf\implies\dfrac{63 + 1470 + 70 + 60}{105} \: x \: = Rs. \: 438500$

$\sf\implies\dfrac{1663}{105} \: x \: = Rs. \: 438500$

$\sf\implies x = 438500 \times \dfrac{105}{1663}$

$\sf \underline{Simplifying \: the \: above \: expression}.$

$\sf\implies x = \dfrac{46042500}{1663}$

$\sf \underline{Now, profit \: share \: of \: each \: partner \: is} :$

$\sf\implies 1^{st} \: patner \: = \dfrac{3}{5}x = \dfrac{3}{5} \times \dfrac{46042500}{1663} \: = Rs. \: 16611.85$

$\sf\implies 2^{nd} \: patner \: = 14x=14\times\dfrac{46042500}{1663}=Rs. \: 3,87,609.7$

$\sf\implies 3^{rd} \: patner \: = \dfrac{2}{3}x = \dfrac{2}{3} \times \dfrac{46042500}{1663} \: = Rs. \: 18457.61$

$\sf\implies 4^{th} \: patner \: = \dfrac{4}{7}x = \dfrac{4}{7} \times \dfrac{46042500}{1663} \: = Rs. \: 15820.81$

muskan Joshi