Question

A and B shared a profit of 24500 rupees in the proportion of 3:7. Each of them gave 2% of his share of the profit to the Soldier's Welfare fund. What was the actual amount given to the find by each of them?

Answer 1

Hint: Assume that the proportion is in x. The share of A and B is Rs. \[3x\] and Rs. \[7x\]. Since it is given that an amount of Rs. 24500 has been shared between A and B, the summation of the share of person A and person B must be equal to Rs. 24500. Now, solve it further and get the value of x. Use the value of x to get the share of A and B. Each of them gave 2% of his share of the profit to the Soldier's Welfare fund. Now, calculate 2% of the share of person A and person B.

Complete step-by-step solution
According to the question, we are given that there are two persons A and B who shared a profit of Rs. 24500 in the proportion 3:7. In addition to this, each of them gave 2% of his share of the profit to the Soldier's Welfare fund.
First of all, let us assume that the proportion is in x.
On transforming the given proportion, we get
\[=3x:7x\] ………………………………(1)
Share of person A = Rs. \[3x\] ……………………………………..(1)
Share of person B = Rs. \[7x\] ……………………………………..(2)
Since it is given that an amount of Rs. 24500 has been shared between A and B so, the summation of the share of person A and person B must be equal to Rs. 24500 …………………………………..(3)
Now, from equation (1), equation (2), and equation (3), we get
\[\begin{align}
  & \Rightarrow 3x+7x+=24500 \\
 & \Rightarrow 10x=24500 \\
 & \Rightarrow x=\dfrac{24500}{10} \\
\end{align}\]
\[\Rightarrow x=2450\] ……………………………………………(4)
On substituting \[x\] by 2450 in equation (1), we get
Share of person A = \[3\times 2450\] = Rs. 7350 …………………………………….(5)
Similarly, on substituting \[x\] by 2450 in equation (2), we get
Share of person B = \[7\times 2450\] = Rs. 17150 …………………………………….(6)
We are also given that both of them donate 2% of their share in the Soldier's Welfare fund.
The amount donated by A = 2% of Rs. 7350 = \[\dfrac{2}{100}\times 7350=\dfrac{735}{5}\] = 147 ………………………………….(7)
The amount donated by B = 2% of Rs. 17150 = \[\dfrac{2}{100}\times 17150=\dfrac{1715}{5}\] = 343 ………………………………….(8)
Therefore, the amount donated by A and B is Rs. 147 and Rs. 343 respectively.

Note: For this type of question, where we are given a ratio and we are given some more information regarding the ratio. For instance, here we are given that an amount of Rs. 24500 is shared between A and B. Approach this type of question by assuming the ratio in x and then calculate the value of x by using all the information provided. This would make the solution easier to approach.