In a partnership A invests \(\frac{1}{4}\)th of the total capital for \(\frac{1}{4}\) of the time, B invests \(\frac{1}{5}\)rd of the total capital for \(\frac{1}{2}\) of the time and C invests the rest of the capital for the whole time. Out of the profit of ₹2280, C's share is:
Answer & explanation
Correct answer: option 1
For \(\frac{1}{4}\), \(\frac{1}{5}\) and \(\frac{1}{2}\):
Let the total capital = 20 Unit, and
Let the total time of investment = 4 months
ATQ,
A : B : C
Inv. : 20 × \(\frac{1}{4}\) : 20 × \(\frac{1}{5}\) : Rest
Time : 4 × \(\frac{1}{4}\) : 4 × \(\frac{1}{2}\) : 4
A : B : C
Inv. : 5 : 4 : 11
Time : 1 : 2 : 4
Profit: 5 : 8 : 44 [Profit ratio = Inv. ratio × Time ratio]
⇒ Total Profit = 57R = 2280
⇒ 1R = 40
⇒ C's Profit = 44R = 44 × 40 = 1760