If P, Q, and R invested in 1 : 2 : 3 and after 6 months P withdrew all of his capital, Q doubled his capital and R halved his capital. After one year out of a total profit of Rs. 13800, what is the 33.33% of R's profit?
Answer & explanation
Correct answer: option 1
Investment of P = 1R
Investment of Q = 2R
Investment of Q' = 4R (after doing double)
Investment of R = 3R
Investment of R' = 1.5R (after doing half)
Profit Ratio = Investment ratio × time ratio
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So, ATQ
P : Q : Q' : R : R'
Investment ⇒ 1 : 2 : 4 : 3 : 1.5
Time ⇒ 6 : 6 : 6 : 6 : 6
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Profit ⇒ 6 : 12 : 24 : 18 : 9
So,
(P) : (Q + Q') : (R + R')
Profit ⇒ 6 : 36 : 27
Now, total profit = 6 + 36 + 27 = 69R = 13800
⇒ 1R = 200
⇒ 33.33% of R's profit = \(\frac{1}{3}\) × 27R ⇒ 9R = 9 × 200 = 1800