X and Y enter into a partnership with capital in the ratio 3 ∶ 5 After 5 months X adds 50% of his capital, while Y withdraws 60% of his capital. What is the share (in Rs. lakhs) of X in the annual profit of Rs. 6.84 lakhs?
A3.12
B3.6
C3.72
D4.2
Answer:
C. 3.72
Read Explanation:
Given:
X and Y enter into partnership with capital in the ratio = 3 ∶ 5
After 5 months,
X's capital = 150% of initial investment of X
Y's capital = 40% of initial investment of Y
Annual profit = Rs. 6.84 lakhs
Formula used:
(X's profit) ∶ (Y's profit) = (X's capital × Time period of investment) ∶ (Y's capital × Time period of investment)
Calculations:
Let X's and Y's initial investment for the first 5 months be 30 and 50
After 5 months,
X's capital for next 7 months = (150/100) × 30 = 45
Y's capital for next 7 months = (40/100) × 50 = 20
(X's profit)/(Y's profit) = [(30 × 5) + (45 × 7)]/[(50 × 5) + (20 × 7)]
⇒ (150 + 315)/(250 + 140)
⇒ 465/390
⇒ 31/26
Total profit = 31 + 26 = 57 units
⇒ (X's profit)/(Total profit) = 31/57
⇒ (X's profit)/6.84 = 31/57
⇒ X's profit = (31/57) × 6.84
⇒ X's profit = 3.72
∴ The profit earned by X is Rs. 3.72 lakhs
