In a partnership A invests \(\frac{1}{6}\)th of the total capital for \(\frac{1}{6}\) of the time, B invests \(\frac{1}{3}\)rd of the total capital for \(\frac{1}{3}\) of the time and C invests the rest of the capital for the whole time. Out of the profit of ₹2300, find the difference b/w A and B's share.
Answer & explanation
Correct answer: option 2
For \(\frac{1}{6}\) and \(\frac{1}{3}\):
Let the total capital = 6 Unit, and
Let the total time of investment = 6 months
ATQ,
A : B : C
Inv. : 6 × \(\frac{1}{6}\) : 6 × \(\frac{1}{3}\) : Rest
Time : 6 × \(\frac{1}{6}\) : 6 × \(\frac{1}{3}\) : 6
A : B : C
Inv. : 1 : 2 : 3
Time : 1 : 2 : 6
Profit: 1 : 4 : 18 [Profit ratio = Inv. ratio × Time ratio]
⇒ Total Profit = 23R = 2300
⇒ 1R = 100
⇒ Difference b/w A and B's Profit = 3R = 3 × 100 = 300