Question : A invests INR 6,00,000 more than B in a business. B invests his capital for $7 \frac{1}{2}$ months, while A invests his capital for $2 \frac{1}{2}$ more months than B. Out of the total profit of INR 12,40,000, if the share of B is INR 2,48,000 less than the share of A, then the capital of B is:
Option 1: INR 45,00,000
Option 2: INR 42,00,000
Option 3: INR 40,00,000
Option 4: INR 48,00,000
Correct Answer: INR 48,00,000
Solution :
Given: Total profit = INR 12,40,000
Let B's share be $x$.
A's share = $x+248000$
A's share + B's share = 1240000
⇒ $x+x+248000=1240000$
⇒ $x=496000$
A's share = 496000 + 248000 = 744000
The profit share of A to B = 744000 : 496000
The profit share of A to B = 3 : 2
Time ratio of A to B = $10 : \frac{15}{2}$ = 4 : 3
According to the question
$\frac{4A}{3B} = \frac{3}{2}$
⇒ $\frac{A}{B} = \frac{9}{8}$
Capital ratio of A to B = 9 : 8
So, (9 – 8) = 1 unit = 6,00,000
⇒ 8 unit = 6,00,000 × 8 = 48,00,000
Hence, the correct answer is INR 48,00,000.
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