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A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B would invest Rs. 8400 for 5 months and C would invest Rs. 10,000 for 3 months. A wants to be the working member for which he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the shares of B in the profit.
A) Rs. 1900
B) Rs. 2660
C) Rs. 2800
D) Rs. 2840

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Last updated date: 13th Jun 2024
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Answer
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Hint:
We know about the meaning of percent. Percent means out of one hundred, for example: 5% is equal to $\dfrac{5}{{100}}$. Calculate the investment of particular A, B, and C by multiplying Rs. And months. After that we find the shares of B in the profit.

Complete step by step solution:
From the given data, the investment of A for 6 months is Rs. 6500. So, the investment of A is the multiplication of months and Rs. That is,
$6500 \times 6 = 39000$
The investment of B for 5 months is Rs. 8400. Now, we calculate the investment of B that is the multiplication of months and Rs.
$8400 \times 5 = 42000$
The investment of C for 3 months is Rs. 10,000. Now, we calculate the investment of C that is the multiplication of months and Rs.
$10000 \times 3 = 30000$
Now, we calculate the ratio of their investments means that the investment of A, B, and C. that is,
$39000:42000:30000 = 13:14:10$
From the question, A wanted to be the working member for which he was to receive 5% of the profits. The profit earned was Rs. 7400.
For managing A received 5% of 7400. That is:
$7400 \times \dfrac{5}{{100}} = 74 \times 5\\
 = 370$
Hence, the profit of A received is 370.
Hence, the balance is $7400 - 370 = 7030$.
Now, we calculate the shares of B from the profit:
$\dfrac{{14}}{{37}} \times 7030 = 14 \times 190\\
 = 2660$

Hence, the shares of B in the profit is 2660. The option B is the correct option.

Note:
Here we may confuse the balance. Balance is calculated by the subtraction of original value and profit value. Ratio means the relationship between two members that is denominator and numerator and we can also express the ratio as a percentage as well as decimal.