A, B and C become partners in a business. A contributes $$\frac{1}{3}$$ rd of the capital for $$\frac{1}{4}$$ th of the time. B contributes $$\frac{1}{5}$$ th of the capital for $$\frac{1}{6}$$ th of the time and C the rest of the capital for the whole time. If the profit is Rs. 1820, then the A's share in profit is ?

Solution(By Examveda Team)

Let the total capital of A, B and C = 15 units
Let total time for investment = 12 units
Now, According to the question,

Capital Investment of A = $$\frac{1}{3} \times 15$$   = 5units
Capital Investment of B = $$\frac{1}{5} \times 15$$   = 3units
Capital Investment of C = 15 - (5 + 3) = 7

A's Capital Invested for time = $$\frac{1}{4} \times 12$$   = 3units
B's Capital Invested for time = $$\frac{1}{6} \times 12$$   = 2units
C's Capital Invested all the time. i.e = 12units

∴ Profit ratio of A : B : C = (5 × 3) : (3 × 2) : (7 × 12)
= 15 : 6 : 84
= 5 : 2 : 28
Total profit = 5 + 2 + 28 = 35 units
Also, total profit = Rs. 1820 (given)
$$\eqalign{ & {\text{35 units}} = {\text{Rs}}{\text{. 1820}} \cr & {\text{1 unit}} = \frac{{1820}}{{35}} = {\text{Rs}}.52 \cr & {\text{Hence A's share in profit}} \cr & = 5{\text{ units}} \cr & = 52 \times 5 \cr & = {\text{Rs}}{\text{. 260}} \cr} $$