Question

In a business, A invested Rs. 25000 and B invested Rs. 24000. As his salary A got \[{{\dfrac{1}{50}}^{th}}\] of the total profit of Rs. 60000 after which the remaining amount was shared among A and B in the ratio of their shares in profit. Find the difference in the shares of both.

Answer 1

Hint: We have A invested Rs. 25000 and B invested Rs. 24000. So, we start by finding the ratio of their investment, then we have A got a salary as \[{{\dfrac{1}{50}}^{th}}\] of the total profit. So, we solve, \[\dfrac{1}{50}\times 60000\] to get the salary of A. Then using \[\dfrac{\text{Ratio of A}}{\text{Total Ratio}}\times \text{ Total Amount left}\] to find the amount of share A get and similarly for B. Once, we have the share of A and B, we subtract them to get our difference.

Complete step-by-step answer:
We are given that A invested Rs. 25000 and B invested Rs. 24000. So, we will first use these to find the ratio of their share. Now,
\[\text{Ratios of their share}=\dfrac{\text{Share of A}}{\text{Share of B}}\]
\[\Rightarrow \text{Ratios of their share}=\dfrac{25000}{24000}\]
On simplifying, we get,
\[\Rightarrow \text{Ratios of share of A and B}=\dfrac{25}{24}\]
Now, we are given that the total profit was 60000. A got \[{{\dfrac{1}{50}}^{th}}\] of the total profit as salary, that means A got \[\dfrac{1}{50}\] of 60000.
\[\Rightarrow \dfrac{1}{50}\times 60000\]
\[\Rightarrow 1200\]
So, A got Rs. 1200 as his salary.
Now, the rest of the money left is 60000 – 1200 = 58800.
We are given that the rest of the money is distributed among A and B in the ratio of their shares.
Therefore, the ratio of their share is 25:24.
So, the amount received by A is \[\dfrac{25}{25+24}\] of 58800.
\[\Rightarrow \dfrac{25}{49}\times 58800\]
On simplifying, we get, Amount received by A = 30,000.
So, the total amount A have will be 30000 + 1200 salary which is Rs. 31200.
Now, the amount received by B will be
\[B=\dfrac{24}{25+24}\times 58800\]
\[\Rightarrow B=24\times 1200\]
On simplifying, we get,
The amount received by B = 28800.
Now, the difference in the amount of A and B will be
Amount of A – Amount of B
\[\Rightarrow 31200-28800\]
On simplifying, we get,
Difference in share = Rs. 2400
Therefore, the difference in their share is Rs. 2400.

Note: The total share of A is the share received after the division between A and B along with the share he gets as salary. So, while finding the difference, we have to join all the shares of A to get the correct difference. To find the share of A, we find the total of the ratio 25 + 24 and then we simplify 58800 into \[\dfrac{25}{25+24}\] to get the amount A have and then use \[\dfrac{24}{25+24}\] of 58800 to get the share of B.