Question

A total of Rs.\[84000\] is invested in a business. Investment of A is Rs.\[4000\] less than that of B and B’s investment is Rs. \[4000\] less than that of C. If A invested his amount for \[5\] months and B and C each for \[4\] months, then out of the total profit Rs.\[63000\], what is the share of A?

Answer 1

Hint:
To find the share of A we should find the values of every member from the total profit and we will find the total value. With the help of the value we will find the ratio of investment and further it will lead to the required share value with the help of the formula given below.

Formula used:
Let us consider the share of profit of three people is \[{\text{a}}:{\text{b}}:{\text{c}}\]
So, the share of the first person is \[\dfrac{a}{{a + b + c}}\] of the total profit.
The share of the second person is \[\dfrac{b}{{a + b + c}}\] of the total profit.
The share of third person is \[\dfrac{c}{{a + b + c}}\] of the total profit.

Complete step-by-step answer:
It is given the total amount of investment Rs. \[84000\].
Also given that the investment of A is Rs. \[4000\] less than that of B and B’s investment is Rs. \[4000\] less than that of C.
Let us consider, the amount of investment for C is Rs. \[x\].
The amount of the investment for B is Rs. \[x - 4000\].
The amount of the investment for A is Rs. \[x - 8000\].
According to the problem, we know that the total investment is the sum of all three, we get
\[x + (x - 4000) + (x - 8000) = 84000\]
Let us now all the terms in left hand side we get,
\[3x - 12000 = 84000\]
By further solving we get,
\[3x = 96000\]
Let us simply the above term by dividing it by 3 on both sides we get,
\[x = \dfrac{{96000}}{3} = 32000\]
So we have found that the investment of C is \[32000\]
Now, the investment of A is Rs. \[32000 - 8000\]\[ = Rs.24000\]
The amount of the investment for B is Rs. \[32000 - 4000 = Rs.28000\].
The amount of investment for C is Rs. \[32000\].
A is invested his amount for \[5\]months and B and C each for \[4\]months.
So, the shares of profit of \[A:B:C\] is:
\[24000 \times 5:28000 \times 4:32000 \times 4\]
By solving the above ratios we get,
\[24000 \times 5:28000 \times 4:32000 \times 4 = 120000:112000:128000\]
\[ = 15:14:16\]
Total profit is Rs. \[63000\]
So, the share of A is found using the formula given: \[\dfrac{{15}}{{15 + 14 + 16}}\]of the total profit.
Hence, we get the share of A is Rs. \[\dfrac{{15}}{{45}} \times 63000\]
Let us the above term to find share of A, we get,
The share of A is Rs. \[21000\].
Therefore, the share for the profit of A is Rs. \[21000\].

Note:
Similarly using the ratio we can find out the share of B and C also.
The share of B is Rs. \[\dfrac{{14}}{{45}} \times 63000 = 19600\]
The share of C is Rs. \[\dfrac{{16}}{{45}} \times 63000 = 22400\]