Question

A started a business with Rs 3750. After 6 months, B deposited Rs 15000 in that buisness. At the end of the year, if profit is Rs 6900, find the money they got​

Answer 1

Given :-

• $\sf \: A \: started \: a \: business \: with \: Rs \: 3750. \: After \\ \sf \: 6 \: months, B deposited \: Rs \:15000 \: in \: that \: buisness. \: \\ \sf \: At \: the \: end \: of \: the \: year, \: profit \: is \: Rs \: 6900$

To Find :-

• $\sf \: How \: much \: money \: they got.$

Solution :-

$\sf\longmapsto A \: started \: a business \: with \: Rs \: 3750 \: for \: 1 \: years.$

As we know that,

1 years = 12 months

$↦ \sf Rs\: 3750 \times 12$

$➡ \sf\bold{\green{Rs\: 45000}}$

$\sf⟼ B \: deposited \: Rs \: 15000 \: in \: that \: buisness \: for \: 6 months. \:$

$↦ \sf Rs\: 15000 \times 6$

$➡ \sf\bold{\green{Rs\: 90000}}$

$\sf \: Now, \: we \: have \: to \: find the \: ratio \: of \: capital \: of \: A \: and \: B :$

⟶ Ratio of capital of A and B :

Given :

• $\sf \: Capital \: of \: A \: = Rs 45000</li><li> \\ \sf \: Capital \: of \: B = Rs 90000$

$↦ \sf 45000 : 90000$

$↦ \sf 45 : 90$

$↦ \sf 9 : 18$

$➦ \sf\bold{\pink{1 : 2}}$

$\sf \: ➲ Total profit = Rs 6900$

$</p><p> \sf \: Then, \: profit \: of \: A :$

$↦ \sf Profit\: of\: A =\: \dfrac{1}{1 + 2} \times 6900$

$↦ \sf Profit\: of\: A =\: \dfrac{1}{\cancel{3}} \times {\cancel{6900}}$

$➠ \sf\bold{\red{Profit\: of\: A\: =\: Rs\: 2300}}$

$\sf \: And \: profit \: of \: B :$

$↦ \sf Profit\: of\: B =\: \dfrac{2}{1 + 2} \times 6900$

$↦ \sf Profit\: of\: B =\: \dfrac{2}{\cancel{3}} \times {\cancel{6900}}$

$↦ \sf Profit\: of\: B =\: 2 \times 2300$

$➠ \sf\bold{\red{Profit\: of\: B =\: Rs\: 4600}}$

$\sf\therefore A \: gets \: Rs \: 2300 and \: B \: gets \: Rs \: 4600.$

Answer 2

$\huge\sf \red{ \pmb{Answer : }}$

Given:-

$A starts a business with a capital of Rs. 3750 for an year.$

And,

$B deposited an amount of Rs. 15000 after 6 months$

That means;

$Ratio of A's capital to B's capital = 3750 × 12 months : 15000 × 6 months$

$⟹ Ratio of A's capital to B's capital = 45000 : 90000$

$⟹ Ratio of A's capital to B's capital = 1 : 2$

$It is also given that;$

$\sf \: Total \: profit \: at \: the \: end \: of \: the \: year \: = Rs. 6900\\ \sf \: Now,$

$✯ Share of A = 1/(1 + 2) × 6900$

$⟹ Share of A = (1/3) * 6900$

$⟹ Share of A = Rs. 2300$

$Similarly;$

$✯ Share of B = (2/3) * 6900$

$\sf⟹ Share \: of \: B \:= Rs. 4600$